Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 17 - Mensuration [Latest edition]

Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height.

If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, find:

1. radius of its base
2. volume of the cylinder

[Use π =  3.14]

Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.

The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder assuming it is open at either end.

The curved surface area of a right circular cylinder is 308 cm². If the ratio of its total surface area and curved area is 2:1, then find its volume.

The volume of a cylinder of height 4 cm is 154 cm³ Find the circumference of its base. 

The volume of a right circular cylinder is 250 cm³. If the height of the cylinder is equal to the diameter of its base, then find its height.

The ratio of the radius of base and height of a cylinder is 3:7. If its volume is 1584 cm³, then find the radius and height of the cylinder.

A geyser is cylindrical in shape whose diameter is 28 cm and height 1.5 m. Neglecting the thickness of its walls, calculate its outer curved surface area.

A geyser is cylindrical in shape whose diameter is 28 cm and height 1.5 m. Neglecting the thickness of its walls, calculate its capacity.

If the volume of a cylinder of height 14 cm is 896π cm³, find its lateral surface area.

The inner radius of a circular well is 1.75 m and it is 10 m deep. Find the cost of plastering its curved surface area at the rate of ₹ 20 per m².

The radii of two circular cylinders are in the ratio 2 : 3 and their heights are in the ratio 3 : 5, find the ratio of their:

1. Volumes 
2. Curved surface areas.

A cylindrical road roller made up of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 cm³ of iron weighs 8 g.

A rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.

(Use π = `22/7`).

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? (Answer correct to the nearest 100 words)

A well with inside diameter 3 m is dug 14 m deep. Earth taken out of it is spread all around to a width of 4 m to form an embankment. Find the height of embankment.

The radius of a solid right circular cylinder increases by 20% and the height decreases by 10%. Find the percentage change in the volume.

The difference between the outer curved surface and the inner curved surface area of a hollow cylinder is 352 cm². If its height is 28 cm and volume of the material in its is 704 cm³, then find its internal curved surface area.

The sum of the outer and inner curved surface areas of a cylinder 14 cm long is 352 cm². Find the outer and the inner radii of the cylinder if the volume of the metal is 176 cm².

Water flows through a cylindrical pipe of internal radius 3.5 cm at 36 km/hr. Calculate the time it would take to fill a cylindrical tank whose radius and height are 35 cm and 1 m.

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars?

A rectangular sheet of paper 44 cm x 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³  of wood has a mass of 0.6 gm.

The area of the base of a right circular cone is 314 cm² and its height is 15 cm. Find the volume of the cone.

The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

The volume of a cone is 18480 cm³. If the height of the cone is 40 cm, find the radius of its base.

A conical paper cup is in the form of a right circular cone with height 5 cm and diameter of the base 4 cm. How much water can it hold?

How many metres of cloth of 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m? (Take π = 22/7)

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]

The height of cone is 16 cm and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone. (Use π = 3.14)

A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length (height) as 20 cm. If each 1 cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob.

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14). 

The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm², find its radius. (Use it 𝜋 = 22/7).

A conical tent is accommodate to 11 persons each person must have 4 sq. metre of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.

A right triangle, whose sides are 6 cm, 8 cm and 10 cm is made to revolve about its side 8 cm. Find the volume and total surface area of the cone so formed. (use π = 3.14)

The volume of a conical tent is 1232 m³ and the area of the base floor is 154 m². Calculate the:

1. radius of the floor
2. height of the tent
3. length of the canvas required to cover this conical tent if its width is 2 m.

A vessel in the form of an inverted cone is filled with water to the brim: Its height is 20 cm and the diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cones submerged?

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be `1/27` of the volume of the given cone, at what height above the base is the section cut? 

A semi-circular lamina of radius 35 cm is folded so that the two bounding radii are joined together to form a cone. Find:

1. the radius of the cone.
2. the lateral surface area of the cone.

Find the surface area of a sphere of radius 10.5 cm. 

Find the surface area of a sphere of radius 5.6 cm.

Find the surface area of a sphere of radius 14 cm.

Find the surface area of a sphere of diameter 1.4 cm.

Find the surface area of a sphere of diameter 21 cm.

Find the surface area of a sphere of diameter 3.5 cm.

The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m. 

Show that the surface area of a sphere is the same as that of the lateral surface of a right circular cylinder that just enclose the sphere.

A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved surfaces.

A hemispherical bowl has inner diameter 11.2 cm. Find the volume of milk it can hold.

The largest sphere is carved out of a cube of side 7 cm. Find the volume of the sphere.

The volume of a sphere is 288π cm³. Find its surface area.

The ratio of the surface areas of two spheres is 9 :16, find the ratio of their:

1. radii 
2. volumes

If the volume of a sphere is 179 `2/3 cm^3` find its surface area.

The surface area of a solid sphere is 1256 cm². It is cut into two hemispheres. Find the total surface area of a hemisphere.(π = 3.14)

The internal and external diameters of a hollow hemispherical vessel are 14 cm and 21 cm respectively. The cost of silver plating of 1 cm² surface is ₹ 0.40. Find the total cost of silver plating the vessel all over.

A hemispherical dome of a building needs to be painted from outside. If the circumference of the base of the dome is 17.6 m, find the cost of painting it at the rate of ₹ 2 per 100 cm².

Three cubes, each with 8 cm edge, are joined end to end. Find the total surface area of the resulting cuboid.

A solid is cylindrical composed with hemispherical ends. If the total height of solid is 100 cm and the height of cylinder is 72 cm, find its total surface area.

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find its inner surface area.

A gulab jamun, contains sugar syrup upto about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see figure). For one gulab jamun, 

A wooden article was made by removing out a hemisphere from each end of a solid cylinder. The height and diameter of base of the cylinder are 10 cm and 7 cm respectively, find the total surface area of the remaining solid.

A cubical wooden block of side 7 cm is surmounted by a largest hemisphere. Find the volume and total surface area of the resulting solid.

A metallic cylinder has a radius of 3 cm and a height of 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of `3/2` cm and its depth is `8/9` cm. Calculate the ratio of the volume of the metal A to the volume of metal B in the solid.

There is a hemispherical roof on the cylindrical room. The maximum height of the room is 20 m. If the inner diameter of the floor is equal to the maximum height of the room, then find the volume of air in the room. (Use л = 3.14)

A sphere is inscribed in a cylinder such that sphere touches the cylinder. Show that the curved surface of sphere is equal to the curved surface area of cylinder.

The following figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other end. Given that common radius = 3.5 cm, the height of the cylinder = 6.5 cm and the total height = 12.8 cm, calculate the volume of the solid, correct to the nearest cm³.

A toy is in the form of a cone mounted on a hemisphere with the same radius. The radius of the base of the cone is 8 cm and height is 6 cm. Find the surface area and the volume of the toy. (Use π = 3.14)

From a solid metallic cylinder with height 10 cm and radius of base 6 cm, a right circular cone of the same height and same base is removed. Find the volume and the surface area of the remaining solid.

A circus tent is cylindrical upto a height of 3m and conical above it. If the diameter of base is 105 m and the slant height of conical part is 53 m, find the total canvas used in the tent.

A wooden toy is in the shape of a cone mounted on a cylinder. The height of cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone is 10 cm. If the radius of base of the cylinder is half of the radius of the base of the cone, find the total surface area of the toy. (Use π = 3.14).

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter a of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboids are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see the following figure).  Use [π = `22/7`]

A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm.

Find:

1. The total surface area (both the halves).
2. The total cost of painting the two halves at the rate of ₹ 30 per cm² `("Use"  π = 22/7)`.
   

A cone of height 30 cm is melted and recast into a cylinder of the same base. Find the height of the cylinder.

The diameter of a metallic sphere is 12 mm. It is melted and recast into a wire of diameter 0.4 mm. Find the length of the wire.

How many balls each of diameter 2 cm can be made by melting a bigger ball of diameter 6 cm?

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Two cones of same height 6 cm and radii 3 cm and 4 cm are melted and recast into a cylinder of base radius 5 cm. Find the height of the cylinder.

The internal and external radii of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recasts into a solid right circular cylinder of base radius 7 cm. Find the height of the cylinder.

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?

Three metallic spherical balls of radii5 cm, 4 cm and 3 cm are melted together and recast into a big spherical ball. Find the radius of the big ball.

A hollow cylinder of external diameter 18 cm, 1 cm thick and 10 cm long is melted and recast into a solid cylinder diameter 2 cm. Find the length of the cylinder.

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?

A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is it to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

A cubical tank of edge 30 cm is completely filled with water. If 2.7 litres of water is taken out from the tank. Find the height of the remaining water inside the tank.

A solid right circular cylinder of radius 8 cm and height 2 cm is melted and cast into a right circular cone of height 3 times that of the cylinder. Find the curved surface of the cone.

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. Use [π = `22/7`]

What is the least number of solid metallic spheres, each 6 cm in diameter, that should be melted to cast a solid metallic cylinder whose height is 53 cm and diameter 6 cm? Also find the total surface area of the cylinder.

Oil is stored in a spherical vessel occupying `3/4` of its full capacity. Radius of this spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm. Find the height of the oil in the cylindrical vessel (correct to the nearest cm). Take π = `22/7`

Volume of a cylinder of height 3 cm is a 48π. Radius of the cylinder is ______.

If a cone, a hemisphere and a cylinder have equal bases and have equal heights, then the ratio of their volumes is ______.

The number of balls of radius 2 cm that can be made from a sphere of radius 6 cm, is ______.

The ratio of the height and radius of a right circular cylinder is 7 : 5 and its volume is 550 cm³. Its radius is ______.

A cone of equal height and equal base is cut off from a cylinder of height 24 cm and base radius 7 cm. The volume of remaining solid is ______.

The surface area of a sphere is 616 cm². Its diameter is ______.

The ratio of the total surface area of a hemisphere and a sphere of same radius is ______.

The volume of a cone is 154 m³ and area of its base is 38.5 m². The cloth required for its curved path is ______.

The curved surface area of a cone of height 12 m is `204(2)/(7)` m². Its slant height is ______.

The total surface area of a cone of base radius and slant height 2l is ______.

A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is ______.

In the following question, two statements, (i) and (ii), are given. Choose the valid statement.

1. The height and radius of a cylinder are 12 cm and 5 cm respectively. Its volume will be 300 π cm³.
2. Volume of sphere is `4/3πr^3`.

In the following question, two statements, (i) and (ii), are given. Choose the valid statement.

1. The circumference of the base of a cylindrical vessel is 132 cm. Its diameter will be 21 cm.
2. Total surface area of a hemisphere = 3πr².

In the following question, two statements, (i) and (ii), are given. Choose the valid statement.

1. The radius and height of a core are in the ratio 3 : 4 and its volume is 301.44 cm³. If π = 3.14, then its radius will be 6 cm.
2. Volume of cylinder = `1/3πr^2h`

In the following question, two statements, (i) and (ii), are given. Choose the valid statement.

1. The total surface area of a sphere is 154 cm². Its radius will be 7 cm.
2. For a cone; h² = l² + r².

A conical tent has the area of base 154 m² and its curved surface area is 550 m², find the volume of the tent.

The height of a cone is 5 cm. Find the height of another cone whose volume is sixteen times its volume and radius equal to its diameter.

A circus tent is cylindrical to a height of 3 m and conical above it. If its diameter is 105 m and slant height of the cone is 53 m, find the total area of canvas required.

A cylindrical vessel 32 cm high and 18 cm radius is filled with sand. This is emptied on the ground and a conical heap of sand is formed. If the height of the heap is 24 cm, find the radius of its base.

The volume of a metallic sphere is 38808 cm³. Find its surface area.

Find the weight of a spherical shell of copper having external diameter 30 cm and thickness of 2 cm. Density of copper is 10 g/cm³.

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Find the volume and surface area of a solid in the form of a right circular cylinder with hemispherical ends whose extreme length is 21 dm and diameter is 2.5 dm.

How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

A rectangular tank of internal dimensions 14 m × 11 m × 8 m is filled with water by a cylindrical pipe in 2 hrs. 15 minutes. If water runs through the pipe at the rate of 5 m/s, find the internal diameter of the pipe.