Question 1

If you have a cylinder and a cone with the same radius and the same height, how many full cones of water would it take to exactly fill the cylinder?

Accepted Answer

3

Answer

1.5

Answer

4

Answer

2

Question 2

If a sphere and a cylinder have the same radius

r

, and the height of the cylinder is equal to the diameter of the sphere (

h = 2r

), what fraction of the cylinder's volume is occupied by the sphere?

Accepted Answer

Two-thirds

Answer

Three-quarters

Answer

One-half

Answer

One-third

Question 3

A student fills a sphere with sand and pours it into a cylinder. Both have the same radius

r

, and the cylinder has a height of

h = 2r

. If the cylinder was initially empty, what is the formula for the volume of the sphere based on this relationship?

Accepted Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Question 4

If a cone and a sphere both have the same radius

r

, and the height of the cone is

h = 2r

, how many of these cones would you need to melt down to create exactly one sphere of the same radius?

Accepted Answer

2

Answer

4

Answer

1.5

Answer

3

Question 5

If a cone has a base radius of

r

and a height of

h = 2r

, and a cylinder has the same radius and height, what is the volume of the cone in relation to the cylinder's volume of

90\pi	ext{ cm}^{3}

?

Accepted Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Question 6

Imagine you have a hollow hemisphere and a hollow cone, both with the same radius

r

. If the height of the cone is also

h = 2r

, how many full cones of water would be needed to fill the hemisphere?

Accepted Answer

2

Answer

3

Answer

1

Answer

1.5

Question 7

If a sphere and a cone have the same radius

r

, and the volume of the sphere is exactly double the volume of the cone, what must be the height,

h = 2r

, of the cone?

Accepted Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Question 8

If a cylinder, a sphere, and a cone all share the same radius

r

, and the height of both the cylinder and the cone is

h = 2r

, what is the ratio of their volumes (Cone : Sphere : Cylinder)?

Accepted Answer

1 : 2 : 3

Answer

1 : 2 : 4

Answer

2 : 3 : 4

Answer

1 : 3 : 2

Question 9

If a cylinder and a cone have equal volumes and the same base radius

r

, what is the relationship between the height of the cylinder (

h = 2r

) and the height of the cone (

90\pi	ext{ cm}^{3}

)?

Accepted Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Question 10

An 8th-grade class performs an experiment where they fill a cone with water and pour it into a cylinder of the same radius and height. They repeat this three times until the cylinder is full. If the volume of the cylinder is

r

, what is the volume of the cone?

Accepted Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

Answer

V = \frac{4}{3}\pi r^{3}

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