Question

(30 points)

Choose all that give the correct measure of volume for the solid shown.


Cone: V ≈ 1256.64 cm3


Sphere: V ≈ 268.08 cm3


Cylinder: V ≈ 50.27 cm3

Answer 1

Cylinder: V ≈
`50.27 cm^3`

Explanation:

We need to find the volume of the three solids.

CONE

The volume of a cone is given as:

`V = (1)/(3) \pi r^2h`

where r = radius

h = height

The radius of the cone is 5 cm (since its diameter is 10 cm) and its height is 12 cm.

Therefore, its volume is:

`V = (1)/(3) \pi * 5^2 * 12 \\\\V = 314.16 cm^3`

SPHERE

The volume of a sphere is given as:

`V = (4)/(3) \pi r^3`

The radius of the sphere is 2 cm (since its diameter is 4 cm).

Therefore, the volume of the sphere is:

`V = (4)/(3) * \pi * 2^3\\\\V = (4)/(3) * \pi * 8\\\\V = 33.51 cm^3`

CYLINDER

The volume of a cylinder is given as:

`V = \pi r^2 h`

The radius of the cylinder is 2 cm and its height is 4 cm.

Therefore, the volume of the cylinder is:

`V = \pi * 2^2 * 4\\\\V = \pi * 4 * 4\\\\V = 50.27cm^3`

The only one that gives the correct measure of the volume of the given shape is the cylinder.