B Nirmala Shastry solutions for मॅथेमॅटिक्स [अंग्रेजी] कक्षा ९ आयसीएसई chapter 18 - Surface Area and Volume of Solids [Latest edition]

Edge of a metal cube is 3 cm. Find the total surface area of the cube.

Edge of a metal cube is 3 cm. A rectangular box is filled with 30 such cubes. Calculate the internal volume of the box.

If the weight of the box is 1.5 kg and the total weight of the box with the thirty cubes is 2.4 kg, calculate the weight of each cube giving your answer in grams.

A solid metal bar is in the shape of a cuboid of length 250 cm and volume 4840 cm³. The cross-section is a square of side x cm. Find x.

A box, cuboid in shape, measures 250 cm by 88 cm by h cm. 120 such metal bars fit exactly in the box. Find h.

How many square glazed tiles of side 8 cm will be required to cover the walls of a room 4 m by 3 m by 2 m? If 25 tiles cost ₹ 40, find the cost of tiling the walls of the room.

The length of a room is double its breadth and height is 3 m. If the area of four walls is 108 m², find the volume of the room.

A 4 cm edge cube is cut into 1 cm edge cubes. Calculate the total surface area of all the small cubes.

From a rectangular sheet of metal 48 cm by 36 cm, a square with side 8 cm is cut off from each of its corners. An open box is made of the remaining sheet. Find the volume of the box. 

A rectangular plot of land measures 41 m in length and 22.5 m in width. A boundary wall 2 m high is built all around the plot at a distance of 1.5 m from the plot. Find the inner surface area of the boundary wall.

The dimensions of a rectangular solid are 36 cm by 75 cm by 80 cm. Find the edge of a cube whose volume is same as that of this solid.

In a rectangular solid l : b : h = 4 : 3 : 2. If the total surface area is 1300 cm², find its dimensions.

In a rectangular solid l : b : h = 5 : 4 : 2. If its volume is 1080 cm³, find the dimensions of the solid.

Find the height of a box if the longest rod that fits in the box is 21 cm and l = 20 cm, b = 5 cm.

Find the length of a box with b = 16 cm, h = 12 cm and the length of the longest rod that fits in the box is 29 cm.

A cube whose edge is 21 cm long has a circle of diameter 21 cm on each of its faces painted black. What is the total area of the unpainted surface of the cube?

The internal measurements of a box are 20 cm long, 16 cm wide and 24 cm high. How many 4 cm cubes can be put into the box?

A rectangular container whose base is a square of side 6 cm holds water up to 3 cm from the top. When a solid cube is placed in the water and is completely submerged, the water rises to the top and 17 cm³ of water overflows. Find the edge of the cube.

A rectangular container with base 8 cm by 5 cm contains some water. When a cube of edge 4 cm is placed in it the water rises in the container. Find the rise in the water level.

The length and breadth of a playground are 24 m by 20 m. Find the cost of covering it with gravel 1.5 cm deep, if the gravel costs ₹ 15 per m³.

Three cubes each with 5 cm edge, are joined end to end. Find the total surface area of the resulting cuboid.

If each side of a cube is increased by 2 cm, the volume increases by 488 cm³. Find the side of the cube.

Three solid metal cubes of sides 6 cm, 8 cm and 10 cm are melted and formed into a new cube. Find the side of the new cube.

A school hall has the dimensions 24 m by 15 m by 6 m. If each child requires 16 m³ of air, how many children can be accommodated in the hall?

A room measures 6 m by 5 m by 4 m. Find the paint required in litres, to paint the walls with 2 coats of paint if a litre of paint is used to cover 18 m² in 1 coat. The windows and doors occupy 10% of the wall area.

The figure alongside represents the horizontal cross-section of a pond. ABDE is an isosceles trapezium in which AE = 1 m, ED = 5 m, BD = 7 m. BCD is a semicircle on diameter BD. The sides of the pond are vertical and the depth of the water in the pond is 50 cm. Find the

1. perimeter of the given cross-section.
2. area of the sides in contact with water.
3. distance between AE and BD.
4. volume of water in the pond.

A certain quality of wood costs ₹ 67,500 per m³. A solid cubical block of such wood is bought for ₹ 4320. Calculate the volume of the block and find the length of one edge of the block.

A hall is 10 m long, 5 m wide and 4 m high. It has one door 2 m by 1 m and 2 windows 1 m by 80 cm. Find the

1. area of the 4 walls (excluding the door and windows).
2. cost of distempering the walls at ₹ 50 per m².
3. cost of polishing the floor at the rate of ₹ 5 per m².

ABCD is the cross-section of a metal container in a paint factory.

If AB = 2.4 m, DC = 1.6 m, BQ = CR = 1.2 m and height of the container is 1.1 m, find 

1. the volume of paint in the container.
2. the cost of paint at ₹ 40 per litre. [1m³ = 1000 litres]

Calculate the quantity of water in a swimming pool which is 50 m long, 12 m wide and the shallow and deep ends are 1.5 m and 3 m respectively.

The square on the diagonal of a cube has an area 363 cm². Calculate the side and the surface area of the cube.

The length of the longest pencil which can fit in a box measuring 6 cm, 3 cm and 2 cm.

A wall measures 10 m by 1.5 m by 2 m. The number of bricks of size 25 cm, 15 cm by 4 cm that are needed to make the wall is ______.

A cube’s length is 5 cm. A box is filled with 30 such cubes. Volume of the box is ______.

The total surface area of a cube is 384 cm² ∴ The volume of the cube is ______.

The volume of a cube is 216 cm³. Its surface area is ______.

Two cubes of edge 3 cm are joined together to form a cuboid. Its surface area is ______.

The length of the longest rod is 13 cm in a box of 12 cm long and 4 cm wide. The height of the box is ______.

The number of tiles of size 10 cm by 6 cm that can fit on a floor 4 m by 3 m is ______.

A metal rod 25 cm, 20 cm, 16 cm is melted to form a cube. The length of the cube is ______.

A school hall has dimensions 24 m by 15 m by 6 m. If each child requires 16 m³ of air, the number of children that can be accommodated in the hall is ______.

Two metal rods of dimensions are 5 cm by 8 cm by 3 cm and 8 cm, 6 cm, 2 cm are melted and formed into a cube. The side of the cube is ______.

Assertion: The dimensions of a cuboid are x, y and z. If xy = 20, yz = 10 and xz = 18, the volume of the cuboid is 60 cubic units.

Reason: The volume of a cuboid = length × breadth × height.

Assertion: From a rectangular sheet 40 cm by 28 cm, a square with side 5 cm is cut off from each of its corners. The volume of the open box formed with the remaining sheet is 2700 cm³.

Reason: Longest diagonal of a cuboid is `sqrt(l^2 + b^2 + h^2)`

Assertion: A closed tank containing some water measures 9 cm by 5 cm by 6 cm. When it is placed with base 6 cm by 5 cm on the height of water in the tank is 3 cm. But when placed on the larger base 9 cm by 5 cm. The height of water is 2 cm.

Reason: Volume of water inside the tank remains the same = Area of base × height of water.

Assertion: Two cubes of side 2 cm are joined together to form a cuboid the surface area of a cuboid is 40 cm².

Reason: The surface area of a cuboid is the sum of the surface areas of the two cubes.

A closed storage container consists of a cuboid ABDEPQST to which a quadrant of a cylinder BCDQRS is attached as shown in the figure. AE = 20 cm, ED = 30 m, DC = 20 cm and CR = 70 cm. Taking π = 3.14, calculate:

1. the area of the face ABCDE
2. the volume of the container
3. the length of arc BC
4. the total surface area

ABCD is the cross-section of a metal container in a paint factory. If AB = 2.4 m, DC = 1.6 m, BQ = CR = 1.2 m, height of the container is 1.1 m. Find the volume of paint in the container.

The outer dimensions of a wooden box are 20 cm, 12 cm and 8 cm. The thickness of the wood is 10 mm. Find (i) the volume of wood and (ii) the cost of the wood required for the box if 1 cm³ of wood costs ₹ 8.50.

A metallic cuboid’s dimensions are 10 cm, 27 cm and 12.5 cm. It is melted and recast into a cube. Find (i) the edge of the cube and (ii) the total surface area of the cube.

ABC is the cross-section of the prism. Find the surface area and volume of the prism if AB = AC = 5 cm, BC = 6 cm and CR = 8 cm.

The diagram represents the floor of a room. All dimensions are in metres and all the angles are right angles. Calculate

1. the perimeter of the room
2. the area of the floor
3. the volume of the room if it is 3 m high.

The length, breadth and height of 2 solid metal rods are 4 cm, 2 cm, 1 cm and 7 cm, 4 cm, 2 cm respectively. These are melted and combined to form a cube. What is the length of the cube?

Each edge of a metal cube measures 3 cm and it weighs 5 kg. What is the length of another cube of same metal weighing 40 kg?

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.

When three equal cubes are joined end to end, the surface area of the resulting cuboid is 504 cm². Find the edge of each cube.

Find the number of bricks with dimensions 15 cm by 9 cm by 5 cm required to build a wall of dimensions 18 m by 0.5 m by 3 m.

A closed rectangular tank with dimensions 4 m by 2 m by 3 m is filled with water to a depth of 1 m as shown in the figure. If the tank is turned so that it rests on its smallest face, find the new depth of water in the tank.

The longest rod that fits into a box is 25 cm. If the length and the breadth of the box are 16 cm and 12 cm, find the height of the box.

The square on the diagonal of a cube has are 147 cm². Find the length of the side and surface area of the cube.