Question

two cones are shown.
how much more volume does the larger cone have than the smaller cone?
answer to the nearest cubic meter and use 3.14 to approximate π.
□ m³

Explanation:

Step1: Recall Cone Volume Formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Calculate Volume of Smaller Cone

For the smaller cone, \( r = 4 \, \text{m} \), \( h = 5 \, \text{m} \), and \( \pi \approx 3.14 \).
Substitute into the formula:
\( V_{\text{small}} = \frac{1}{3} \times 3.14 \times 4^2 \times 5 \)
\( = \frac{1}{3} \times 3.14 \times 16 \times 5 \)
\( = \frac{1}{3} \times 251.2 \)
\( \approx 83.73 \, \text{m}^3 \)

Step3: Calculate Volume of Larger Cone

For the larger cone, \( r = 4 \, \text{m} \), \( h = 7 \, \text{m} \), and \( \pi \approx 3.14 \).
Substitute into the formula:
\( V_{\text{large}} = \frac{1}{3} \times 3.14 \times 4^2 \times 7 \)
\( = \frac{1}{3} \times 3.14 \times 16 \times 7 \)
\( = \frac{1}{3} \times 351.68 \)
\( \approx 117.23 \, \text{m}^3 \)

Step4: Find the Difference in Volumes

Subtract the volume of the smaller cone from the larger one:
\( \Delta V = V_{\text{large}} - V_{\text{small}} \)
\( \approx 117.23 - 83.73 \)
\( = 33.5 \approx 34 \, \text{m}^3 \) (rounded to the nearest cubic meter)

Answer:

\( 34 \)