###### Advertisements

###### Advertisements

A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

###### Advertisements

#### Solution

Let *r* and *h* be the radius and depth of the well, respectively.

`:.r=4/2=2m ` and *h* = 21 m

Let *R* and *H* be the outer radius and height of the embankment, respectively.

∴ *R* = *r* + 3 = 2 + 3 = 5 m

Now

Volume of the earth used to form the embankment = Volume of the earth dug out of the well

`pi(R^2-r^2)H=pir^2h`

`=>H=(r^2h)/(R^2-r^2)`

`=>H=(2^2xx21)/(5^2-2^2)=4m`

Thus, the height of the embankment is 4 m.

#### APPEARS IN

#### RELATED QUESTIONS

In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km^{2}, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.

A solid sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is ______.

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm^{2}. [Use π = 3.14]

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

Find the volume of a sphere of diameter 6 cm.

Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.

Find the surface area of a sphere of radius 7 cm.

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm, and 30 cm respectively. How many balls were melted to make the tube?

A metal parallelopiped of measures 16 cm x 11 cm x 10 cm was melted to make coins. How many coins were made if the thickness and diameter of each coin were 2 mm and 2 cm respectively?

The diameter and length of a roller is 120 cm and 84 cm respectively. To level the ground, 200 rotations of the roller are required. Find the expenditure to level the ground at the rate of Rs. 10 per sq.m.

Radius of a sphere is 14 cm. Find the surface area of the sphere.

A tank of cylindrical shape has radius 2.8 m and its height 3.5 m. Complete the activity to find how many litres of water the tank will contain.

Capacity of water tank = Volume of cylindrical tank

= πr^{2}h

An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5 gm.

The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is

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

How many solid cylinders of radius 6 cm and height 12 cm can be made by melting a solid sphere of radius 18 cm?

**Activity:** Radius of the sphere, r = 18 cm

For cylinder, radius R = 6 cm, height H = 12 cm

∴ Number of cylinders can be made =`"Volume of the sphere"/square`

`= (4/3 pir^3)/square`

`= (4/3 xx 18 xx 18 xx 18)/square`

= `square`

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm^{3 }. the radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it.

The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.

If the side of a cube is 5 cm, then find its volume.

In the above figure, a sphere is placed in a cylinder. It touches the top, bottom and curved surface of the cylinder. If the radius of the base of the cylinder is ‘r’, write the answer to the following questions.

a. What is the height of the cylinder in terms of ‘r’?

b. What is the ratio of the curved surface area of the cylinder and the surface area of the sphere?

c. What is the ratio of volumes of the cylinder and of the sphere?

Tick the object which has more volume

Arrange the given objects according to their volume

Arrange the given objects according to their volume

Arrange the given objects according to their volume

A metal cuboid of measures 16 cm × 11 cm × 10 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively? (π = 3.14)

The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. then height of bucket is ______.

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?

If R is the radius of the base of the hat, then the total outer surface area of the hat is ______.

______ surface area of room = area of 4 walls.

Ratio of area of a circle to the area of a square whose side equals radius of circle is 1 : π.

Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.

There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, find the diameter of the pond.

A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.

A boy is cycling such that the wheels of the cycle are making 140 revolutions per hour. If the diameter of the wheel is 60 cm, calculate the speed in km/h with which the boy is cycling

The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?

A rectangular examination hall having seats for 500 candidates has to be built so as to allow 4 cubic metres of air and 0.5 square metres of floor area per candidate. If the length of hall be 25 m, find the height and breadth of the hall.

If the length of the diagonal of a cube is `5sqrt(3)` cm, find the total surface area.

Length of the diagonal of the cube = `square`

So, `square` = `5sqrt(3)`

⇒ Side = `square`

Total surface area of cube = `square`

= `square` × `square` × `square`

= `square` cm^{2}

Hence, the total surface area is `square`.

Find the surface area of a sphere of radius 7 cm.

**Solution :**

The surface area of the sphere = 4πr^{2}

= `4 xx 22/7 xx square^2`

= `4 xx 22/7 xx square`

= `square xx 7`

∴ The surface area of the sphere = `square` sq.cm.