Question

An igloo can be modeled as a hemisphere. Its radius measures 4 m. Find its volume in cubic meters. Round your answer to the nearest tenth if necessary.
Answer
Attempt 1 out of 2

Answer 1

To find the volume of a hemisphere (half of a sphere), you can use the formula for the volume of a sphere and then take half of it. The formula for the volume \( V \) of a sphere with radius \( r \) is:

\[
V = \frac{4}{3} \pi r^3
\]

For a hemisphere, the volume \( V_{\text{hemisphere}} \) is:

\[
V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3
\]

Given that the radius \( r = 4 \, \text{m} \), we can substitute this value into the formula:

\[
V_{\text{hemisphere}} = \frac{2}{3} \pi (4)^3
\]

First, calculate \( (4)^3 \):

\[
(4)^3 = 64
\]

Now substitute this back into the volume formula:

\[
V_{\text{hemisphere}} = \frac{2}{3} \pi (64)
\]

This simplifies to:

\[
V_{\text{hemisphere}} = \frac{128}{3} \pi
\]

Now, we can approximate the volume using \( \pi \approx 3.14 \):

\[
V_{\text{hemisphere}} \approx \frac{128}{3} \times 3.14 \approx 42.6667 \times 3.14 \approx 134.041
\]

Finally, rounding the answer to the nearest tenth, we have:

\[
V_{\text{hemisphere}} \approx 134.0 \, \text{m}^3
\]

Thus, the volume of the igloo modeled as a hemisphere is approximately **134.0 cubic meters**.