Question

Question

Use the image to answer the question.

A 3-dimensional cone is placed on top of a 3-dimensional cylinder. One of the cylinder bases is common to the cone, with the same circumference.

A 3D modeler is designing a component of a castle in a video game. She places a cone on top of a cylinder so they line up and share the same radius. The cone and the cylinder share the same height. If the volume of the cone is 50 cm3
, what is the volume of the whole object?

(1 point)
cm3

Answer 1

Volume of a cone = (1/3) × π × r^2 × h
Volume of a cylinder = π × r^2 × h

Since the cone and cylinder have the same radius and height, the total volume would be the sum of the volumes of the cone and the cylinder.

Total volume = (1/3) × π × r^2 × h + π × r^2 × h
Total volume = (1/3 × π × r^2 + π × r^2) × h
Total volume = (4/3 × π × r^2) × h

Given that the volume of the cone is 50 cm^3, we have:
(1/3) × π × r^2 × h = 50
4/3 × π × r^2 × h = 150
4 × π × r^2 × h = 150
r^2 × h = 150/(4 × π)
r^2 × h = 150/12.57
r^2 × h ≈ 11.93
r^2 ≈ 11.93/h

Substitute the expression for r^2 in the total volume equation:
Total volume ≈ (4/3 × π × 11.93/h) × h
Total volume ≈ 15.91 cm^3

Therefore, the volume of the whole object is 15.91 cm^3.