Surface Areas and Volumes Maths - Surface Areas and Volumes

A cylindrical piece of maximum volume has to be cut out of an iron cube of edge 4cm. Then, the maximum volume of the iron cylinder is:

The total surface area of a cube is 96cm². The volume of the cube is:

Volume of a cuboid is 12cm³. The volume (in cm³) of a cuboid whose side are doubled of the above cuboid is:

Write the correct answer in the following:
The number of planks of dimensions (4m × 50cm × 20cm) that can be stored in a pit which is 16m long, 12m wide and 4m deep is:

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.

Find the amount of water displaced by a solid spherical ball of diameter 28 cm.

Find the volume of a sphere whose radius is 0.63 m.

Find the volume of a sphere whose radius is 7 cm.

This is the picture of an ice-cream cone.

The radius of the cone is 4 cm and the height is 15 cm.
An ice-cream seller keeps 1/4of it empty.
What is the volume (in cm³) of the empty part of the cone?

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the

1. radius r' of the new sphere, and
2. ratio of S and S'.

Find the volume of a sphere whose surface area is 154 cm².

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs. 4989.60. If the cost of white-washing is Rs. 20 per square metre. Find the

1. inside surface area of the dome.
2. Volume of the air inside the dome.

The diameter of the moon is approximately one-fourth the diameter of the earth. What fraction is the volume of the moon of the volume of the earth?

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

A right triangle ABC with its sides 5 cm, 12 cm, and 13 cm is revolved about the side 12 cm. Find the volume of the solid so formed. If the triangle ABC is revolved about side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

The diameter of the moon is approximately one fourth the diameter of the earth. Find the ratio of their surface areas.

Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The top of the hut is a cone with radius 4 m and height 1 m. It is made of economical material. The loor of the tent is covered with rugs.
The total height of the tent is 4.5 m. The cuboidal part of the tent is 6 m long and 5 m wide.
1. What is the outer surface area (in m²) of the hut?
  A. 77
  B. 77+4π√17
  C. 137+4π√17
  D. 137+4π(4+√17)
2. The length and width of a rug used for the loor are 2.6 m and 2 m respectively.
What is the minimum number of rugs required to cover the loor of the tent house? 

A company manufactures wooden boxes. Given below is the picture of an open wooden box. 

The height of the box is 25 cm.
7. What is the surface area (in cm²) of the box?
  A. 3500
  B. 4700
  C. 5900
  D. 30000
8. A shopkeeper store cubes in it.
The side length of one cube is 9 cm.
What would be the maximum number of cubes the shopkeeper can store in a box? (All cubes should be inside the box.)
9. Rajan packs a football into a cubical cardboard box. The radius of the football is 11 cm. Rajan keeps a margin of 1 cm from all the sides of the box while packing.
What is the side length of the cardboard box? 
  A. 11 cm
  B. 20 cm
  C. 22 cm
  D. 24 cm

This is the picture of a gas balloon illed with helium gas.

This balloon has 18 faces that are square in shape and 8 equilateral faces that are triangular.
3. Which of the following is the net of the balloon?

4. The side length of the square is 20 cm. What is the total surface area of the balloon?

Raghav bought this planter.

The radius of the rim is 14 cm. The curved surface area of the planter is 1848 cm².
5. What is the height of the planter?
6. What is the volume of the planter?

Read the passage given below and answer any four questions:
Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length 4m, width 2m and the height 3m as shown in the following figure.
The room was separate at the roof of the house. The dimensions of the bricks used are: 25cm × 10cm × 5cm.

1. Total how many bricks will be required? (1m³ =1000000cm³):

1. 30000
2. 40000
3. 28800
4. 27000

2. How many bricks will be used on both walls along the length (length = 4m)?

1. 19200
2. 20200
3. 18800
4. 17000

3. How many bricks will be used on both walls along the width (width = 3m)?

1. 19200
2. 9600
3. 10000
4. 15000

4. What is the volume of the room?

1. 24m³
2. 12m³
3. 20m³
4. 15m³

5. What is the area of the floor?

1. 10m²
2. 12m²
3. 8m²
4. 8m³