Cones, Cylinders, & Spheres Online Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
The volume of a cylinder is 60 cm3
. What is the volume of a cone that shares the same radius and height as the cylinder?(1 point)
Responses

90 cm3
90 cm cubed

20 cm3
20 cm cubed

40 cm3
40 cm cubed

180 cm3

Answer 1

The volume of a cone is given by the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

The volume of a cylinder is given by the formula:

\[ V = \pi r^2 h \]

From the information provided, the volume of the cylinder is 60 cm³.

Since the cone shares the same radius (r) and height (h) as the cylinder, we can relate the volume of the cone to the volume of the cylinder. The volume of the cone is one-third of the volume of the cylinder:

\[ V_{cone} = \frac{1}{3} V_{cylinder} \]

Now, substituting the volume of the cylinder:

\[ V_{cone} = \frac{1}{3} \times 60 , \text{cm}^3 = 20 , \text{cm}^3 \]

Therefore, the volume of the cone is 20 cm³.