Question 1

A solid metallic sphere of radius

6	ext{ cm}

is melted and recast into the shape of a solid cylinder of radius

4	ext{ cm}

. What is the height of the resulting cylinder?

Accepted Answer

18 cm

Answer

12 cm

Answer

9 cm

Answer

24 cm

Question 2

If the radius of a right circular cone is doubled and its height is halved, how does the new volume compare to the original volume?

Accepted Answer

It is doubled

Answer

It remains the same

Answer

It is quadrupled

Answer

It is tripled

Question 3

A right circular cylinder and a right circular cone have the same radius

6	ext{ cm}

and the same height

4	ext{ cm}

. What is the ratio of the volume of the cylinder to the volume of the cone?

Accepted Answer

3:1

Answer

3:2

Answer

1:3

Answer

2:1

Question 4

What is the total surface area of a solid hemisphere of radius

6	ext{ cm}

? (Use

4	ext{ cm}

)

Accepted Answer

462 sq cm

Answer

154 sq cm

Answer

308 sq cm

Answer

616 sq cm

Question 5

A cylinder and a cone have equal radii and equal volumes. What is the ratio of the height of the cylinder to the height of the cone?

Accepted Answer

1:3

Answer

3:1

Answer

1:1

Answer

1:9

Question 6

The surface area of a sphere is

6	ext{ cm}

. What is its volume? (Use

4	ext{ cm}

)

Accepted Answer

1437.33 cubic cm

Answer

1078.67 cubic cm

Answer

1232.00 cubic cm

Answer

924.00 cubic cm

Question 7

If a right circular cone has a height of

6	ext{ cm}

and a slant height of

4	ext{ cm}

, what is its curved surface area? (Use

\pi = 3.14

)

Accepted Answer

47.1 sq cm

Answer

75.36 sq cm

Answer

37.68 sq cm

Answer

62.8 sq cm

Question 8

Two spheres have their surface areas in the ratio

6	ext{ cm}

. What is the ratio of their volumes?

Accepted Answer

27:64

Answer

9:16

Answer

81:256

Answer

3:4

Question 9

A solid right circular cone of height

6	ext{ cm}

and base radius

4	ext{ cm}

is melted and recast into the shape of a sphere. What is the radius of this sphere?

Accepted Answer

6 cm

Answer

12 cm

Answer

3 cm

Answer

4 cm

Question 10

If a right circular cylinder has a radius of

6	ext{ cm}

and a total surface area of

4	ext{ cm}

, what is its height? (Use

\pi = 3.14

)

Accepted Answer

15 cm

Answer

12 cm

Answer

10 cm

Answer

20 cm

Question 11

A solid metallic sphere of radius

6	ext{ cm}

is melted and recast into the shape of a solid cylinder of radius

4	ext{ cm}

. What is the height of the resulting cylinder?

Accepted Answer

32 cm

Answer

24 cm

Answer

36 cm

Answer

16 cm

Question 12

A right circular cone and a cylinder have equal bases and equal heights. If the volume of the cylinder is

6	ext{ cm}

, what is the volume of the cone?

Accepted Answer

48 cm³

Answer

432 cm³

Answer

36 cm³

Answer

72 cm³

Question 13

If the radius of a sphere is doubled, by what factor does its surface area increase?

Accepted Answer

4

Answer

16

Answer

2

Answer

8

Question 14

A cone and a hemisphere have equal bases and equal volumes. What is the ratio of the height of the cone to the radius of its base?

Accepted Answer

2:1

Answer

1:2

Answer

1:1

Answer

3:1

Question 15

A solid cylinder of radius

6	ext{ cm}

and height

4	ext{ cm}

is melted to form small solid spheres, each of radius

\pi = 3.14

. How many such spheres can be formed?

Accepted Answer

3000

Answer

2940

Answer

2500

Answer

3150

Question 16

The total surface area of a solid hemisphere of radius

6	ext{ cm}

is equal to the curved surface area of a cylinder of the same radius. What is the height of the cylinder in terms of

4	ext{ cm}

?

Accepted Answer

1.5r

Answer

3r

Answer

2r

Answer

r

Question 17

The radii of two cylinders are in the ratio

6	ext{ cm}

and their heights are in the ratio

4	ext{ cm}

. What is the ratio of their volumes?

Accepted Answer

20:27

Answer

10:9

Answer

4:9

Answer

20:9

Question 18

If a right circular cone has a height of

6	ext{ cm}

and a slant height of

4	ext{ cm}

, what is the curved surface area of the cone in terms of

\pi = 3.14

?

Accepted Answer

65\pi 	ext{ cm}^2

Answer

60\pi 	ext{ cm}^2

Answer

156\pi 	ext{ cm}^2

Answer

90\pi 	ext{ cm}^2

Question 19

If the volume and the surface area of a sphere are numerically equal, what is the diameter of the sphere?

Accepted Answer

6 units

Answer

4 units

Answer

2 units

Answer

3 units

Question 20

A solid cylinder, a solid cone, and a solid hemisphere have the same base radius

6	ext{ cm}

and the same height

4	ext{ cm}

(where

\pi = 3.14

for the hemisphere). What is the ratio of their volumes in the order Cylinder : Cone : Hemisphere?

Accepted Answer

3 : 1 : 2

Answer

3 : 2 : 1

Answer

2 : 1 : 3

Answer

1 : 2 : 3

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