Worksheet

1.

A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between?

A) 20.48 cu cm B) 30.48 cu cm C) 25.46 cu cm D) None of these

2.

A cylindrical pillar is 50 cm in diameter and 3.5 cm in height. Find the cost of painting the curved surface of pillar at the rate of Rs 12.50 per m²?

A) Rs 56.80 B) Rs 68.75 C) Rs 78.65 D) Rs 72.25

3.

A container has a radius of 3.5 cm and its height is 40 cm. What capacity of water it can store?

A) 1.54 liters B) 3.08 liters C) 4.34 liters D) None of these

4.

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of 10 per m² is 15000, find the height of the hall

A)

7

B)

6

5.

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14cm?

A) 718.66 cu cm B) 818.66 cu cm C) 618.66 cu cm D) 918.66 cu cm

6.

Choose the correct option: A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is _______.

A) 2.1cm B) 4.2cm C) 8.4cm D) None of these

7.

1.) The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

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

(i) inside surface area of the dome, (ii) volume of the air inside the dome.

3.) Monica has a piece of canvas whose area is 551 m2 . She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2 , find the volume of the tent that can be made with it

A)

1.) 7920

2) (i) 249.48 m² (ii) 523.9 m³ (approx.)

3) 1232 m³

B)

1.) 8020

2) (i) 249.48 m² (ii) 523.9 m³ (approx.)

3) 1532 m³

8.

Dimension of a room is 10m X 8m X 3.3m. How many men can be accompanied in this room if each man requires 3 cube m of space?

A) 77 B) 88 C) 33 D) 22

9.

Fill in the blanks: In a cone, if radius is halved and height is doubled, the curved surface area will be ______.

A) Doubled B) Halved C) Remains same D) None of these

10.

Find the maximum length of the rod that can be kept in cuboidal box of sides 30cm, 20cm and 10cm?

A) 2â??400 B) â??1400 C) 700 D) None of these

11.

1.) The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

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

(i) inside surface area of the dome, (ii) volume of the air inside the dome.

3.) Monica has a piece of canvas whose area is 551 m2 . She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2 , find the volume of the tent that can be made with it

A)

1.) 7920

2) (i) 249.48 m² (ii) 523.9 m³ (approx.)

3) 1232 m³

B)

1.) 8020

2) (i) 249.48 m² (ii) 523.9 m³ (approx.)

3) 1532 m³

12.

Diagonal of a cube measures 4√3 cm. Find its volume?

A) 8 cu cm B) 27 cu cm C) 16 cu cm D) 64 cu cm

13.

Find the diameter of a sphere whose surface area is 154 sq. cm.

A) 14 cm B) 3.5 cm C) 7 cm D) 28 cm

14.

Find the lateral surface area of a cube of edge 10 m.

A) 40 sq. m B) 20 sq. m C) 80 sq. m D) 160 sq. m

15.

State True/False: If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : ?.

A) true B) false

16.

Fill in the blanks: If a plane cuts a sphere into two equal position then each portion is _________.

A) Hemisphere B) Segment C) Circle D) None of these

17.

Two spheres each of 5m radius are melted down and recast into a cone of height equal to radius of its base. Find the height of cone.

A) 100m B) 1m C) 20m D) 10m

18.

Volume of a right circular cone is 9856 cm3.If its radius of base is 14 cm, find its curved surface area.

A) 1100 sq. cm B) 4400 sq. cm C) 2200 sq. cm D) 6600 sq. cm

19.

State True/False: Curved surface area of cone is ?rl.

A) true B) false

20.

Fill in the blanks: The line joining the vertex of a cone to the boundary line of the base is called ________.

A) Height B) Length C) Slant Height D) Perimeter