Question

two cylinders are shown.

(image of two cylinders: smaller cylinder with r = 4 m, h = 3 m; larger cylinder with r = 4 m, h = 9 m)

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

Explanation:

Step1: Recall cylinder volume formula

The volume of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Calculate volume of larger cylinder

For the larger cylinder, \( r = 4 \, \text{m} \) and \( h = 9 \, \text{m} \). Using \( \pi \approx 3.14 \), we have:
\( V_{\text{large}} = 3.14 \times 4^2 \times 9 \)
\( = 3.14 \times 16 \times 9 \)
\( = 3.14 \times 144 \)
\( = 452.16 \, \text{m}^3 \)

Step3: Calculate volume of smaller cylinder

For the smaller cylinder, \( r = 4 \, \text{m} \) and \( h = 3 \, \text{m} \). Using \( \pi \approx 3.14 \), we have:
\( V_{\text{small}} = 3.14 \times 4^2 \times 3 \)
\( = 3.14 \times 16 \times 3 \)
\( = 3.14 \times 48 \)
\( = 150.72 \, \text{m}^3 \)

Step4: Find the difference in volumes

Subtract the volume of the smaller cylinder from the larger one:
\( \Delta V = V_{\text{large}} - V_{\text{small}} \)
\( = 452.16 - 150.72 \)
\( = 301.44 \, \text{m}^3 \)
Rounding to the nearest cubic meter, we get \( 301 \, \text{m}^3 \) (since \( 301.44 \approx 301 \)).

Answer:

\( 301 \)