Given below are the

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

1) A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

a) 20 cm

b) 28.44 cm

c) 26.44 cm

d) None of the above

Answer (b)

2) Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm.

Answer (190.93cm

3) A cone, a hemi-sphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes as well

a) 3:2:1

b) 2:4:8

c) 1:2:3

d) 3:9:27

Answer (c)

4) Find the ratio of their total surface areas

a) (√2+1):3:4

b) 2:4:8

c) 1:2:3

d) 3:9:27

Answer (a)

5) A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the one is 2cm and diameter of the base is 4cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.

Answer 8π cm

6) A hemispherical tank full of water is emptied by a pipe at the rate of 3 litres per second. How much time will it take to make the tank half empty, if the tank is 3m in diameter?

Answer (16.5 min)

7) A toy is in the shape of a right circular cylinder with a hemisphere at one end and a cone on the other. The radius and height of the cylindrical part are 5cm and 13cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30cm

Answer

770cm

Answer

i) True

ii) false

iii) True

iv) False

9) The radii of the internal and the external surfaces of metallic spherical shells are 3cm and 3cm respectively. It is melted and recast into a solid right circular cylinder of height 10 cm. Find the diameter of the base of the cylinder

Answer (7 cm)

10) A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of < 5 per 100 sq. cm. [ Use π

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