If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

(a)

4\(\pi\)r² sq.units

(b)

6\(\pi\)r² sq.units

(c)

3\(\pi\)r² sq.units

(d)

8\(\pi\)r² sq.units

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a)

1:2

(b)

1:4

(c)

1:6

(d)

1:8

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

(a)

5600\(\pi\) cm³

(b)

1120\(\pi\) cm³

(c)

56\(\pi\) cm³

(d)

3600\(\pi\) cm³

The total surface area of a hemi-sphere is how much times the square of its radius.

(a)

\(\pi\)

(b)

4\(\pi\)

(c)

3\(\pi\)

(d)

2\(\pi\)

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

(a)

3328\(\pi\) cm³

(b)

3228\(\pi\) cm³

(c)

3240\(\pi\) cm³

(d)

3340\(\pi\) cm³

A spherical ball of radius r₁ units is melted to make 8 new identical balls each of radius r₂ units. Then r₁:r₂ is

(a)

2:1

(b)

1:2

(c)

4:1

(d)

1:4

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

(a)

1:3

(b)

1:2

(c)

2:1

(d)

3:1

The radius of base of a cone 5 cm and height is 12 cm. The slant height of the cone ___________

(a)

13 cm

(b)

17 cm

(c)

7 cm

(d)

60 cm

A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

(a)

3:1:2

(b)

3:2:1

(c)

1:2:3

(d)

1:3:2

The volume of a frustum if a cone of height L and ends-radio and r₁ and r₂ is ___________

(a)

\(\frac{1}{3}\)πh1(r₁²+r₂²+r₁r₂)

(b)

\(\frac{1}{3}\)πh(r₁²+r₂²-r₁r₂)

(c)

πh(r₁²+r₂²+r₁r₂)

(d)

πh(r₁²+r₂²-r₁r₂)

It S₁ denotes the total surface area of a sphere of radius r and S₂ denotes the total surface area of a cylinder of base radius r and height 2r, then ___________

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

(a)

3 times

(b)

6 times

(c)

9 times

(d)

27 times

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is ___________

(a)

15 cm

(b)

12 cm

(c)

10 cm

(d)

17 cm

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

(a)

10 cm

(b)

15 cm

(c)

18 cm

(d)

24 cm

When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as \(\frac { 1 }{ 3 } \). What is the radius of the sphere?

(a)

24 cm

(b)

9cm

(c)

54cm

(d)

4.5cm