Question

A model of a volcano that is 22 cm tall with a volume of 586.7 cubic centimeters. What is the area of the base of the model? Round the answer to the nearest tenth. Pick one
26.7 centimeters squared
80.0 centimeters squared
1,760.1 centimeters squared
4,302.5 centimeters squared

Answer 1

To find the area of the base of the volcano model, we can use the formula for the volume of a cone, which is given by:

\[
V = \frac{1}{3} \times A \times h
\]

Where:
- \( V \) is the volume of the cone,
- \( A \) is the area of the base,
- \( h \) is the height of the cone.

We can rearrange the formula to solve for \( A \):

\[
A = \frac{3V}{h}
\]

Given:
- \( V = 586.7 \, \text{cm}^3 \)
- \( h = 22 \, \text{cm} \)

Now we can substitute the values into the equation:

\[
A = \frac{3 \times 586.7}{22}
\]

Calculating this:

\[
A = \frac{1760.1}{22} \approx 80.0 \, \text{cm}^2
\]

Thus, the area of the base of the model, rounded to the nearest tenth, is:

**80.0 centimeters squared**