Question 1

A solid metal cone with a radius of

3

cm and a height of

10

cm is melted down and recast into a sphere. What is the radius of the resulting sphere?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

cm (approx

1.96

cm)

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Question 2

A cylindrical water tank has a radius of

3

meters and a height of

10

meters. If a heavy spherical ball with a radius of

1

meter is dropped into the tank and is completely submerged, what is the new total volume occupied by the water and the ball inside the tank?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

cubic meters

Answer

22.67\pi

Answer

24.00\pi

Answer

21.00\pi

Question 3

A square pyramid has a base with a side length of

3

cm and a slant height of

10

cm. What is the volume of this pyramid?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Question 4

A right rectangular prism has a base with dimensions

3

cm by

10

cm. A cone has a circular base with a radius of

1

cm. If both solids have the same volume, what is the ratio of the height of the prism to the height of the cone?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

to

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

to

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

to

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

to

1.96

Question 5

A hollow sphere has an outer radius of

3

cm and an inner radius of

10

cm. What is the volume of the material used to make the sphere?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Question 6

A cylindrical container with a radius of

3

and a height of

10

is filled to the brim with water. A heavy sphere with a radius of

1

is carefully lowered into the cylinder until it rests at the bottom. What fraction of the original water remains in the cylinder?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

Answer

3^{2/3} 	imes 2.5^{1/3}

Answer

3^{2/3} 	imes 2.5^{1/3}

Answer

3^{2/3} 	imes 2.5^{1/3}

Question 7

A right circular cone and a cylinder have the same radius

3

and the same volume. If the height of the cylinder is

10

cm, what is the height of the cone?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Answer

3^{2/3} 	imes 2.5^{1/3}

cm

Question 8

A hemispherical bowl with an internal radius of

3

cm is completely full of liquid. This liquid is to be poured into cylindrical bottles of radius

10

cm and height

1

cm. How many such bottles are required to empty the bowl?

Accepted Answer

18

Answer

36

Answer

54

Answer

27

Question 9

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

Accepted Answer

8

Answer

2

Answer

16

Answer

4

Question 10

A solid object is composed of a cylinder with a height of

3

cm and a radius of

10

cm, topped with a cone of the same radius and a height of

1

cm. What is the total volume of this composite solid?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Question 11

An equilateral triangular prism has a base edge of

3

cm and a length of

10

cm. What is the volume of the prism?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Question 12

A right square pyramid has a base edge of

3

cm and a slant height of

10

cm. What is the volume of this pyramid?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Question 13

A cylinder and a cone have the same radius

3

and the same height

10

. If the volume of the cylinder is

1

cubic centimeters, what is the volume of the cone?

Accepted Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

Answer

3^{2/3} 	imes 2.5^{1/3}

1.96

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