UpStudy Free Solution:

To find the volume of a hemisphere, you can use the formula for the volume of a sphere and then divide by 2:

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

Given that the radius \(r\) is 5.9 meters, we can plug this value into the formula:

\[V = \frac { 2} { 3} \pi ( 5.9) ^ 3\]

First, calculate \(( 5.9) ^ 3\):

\[( 5.9) ^ 3 = 5.9 \times 5.9 \times 5.9 = 205.379\]

Now, multiply this result by \(\frac { 2} { 3} \pi \):

\[V = \frac { 2} { 3} \pi \times 205.379\]

Using \(\pi \approx 3.14159\):

\[V \approx \frac { 2} { 3} \times 3.14159 \times 205.379\]

First, calculate \(\frac { 2} { 3} \times 3.14159\):

\[\frac { 2} { 3} \times 3.14159 \approx 2.09439\]

Now, multiply by 205.379:

\[V \approx 2.09439 \times 205.379 \approx 430.1\]

So, the volume of the igloo is approximately \(\boxed{ 430.1} \) cubic meters.

Supplemental Knowledge

In geometry, calculating the volume of three-dimensional shapes is a fundamental concept. For a hemisphere, which is half of a sphere, the volume can be derived from the volume formula for a sphere.

Key Concepts:

1. Volume of a Sphere: The formula to calculate the volume of a sphere is \(V = \frac { 4} { 3} \pi r^ 3\), where \(r\) is the radius.

2. Volume of a Hemisphere: Since a hemisphere is half of a sphere, its volume is half that of the sphere:

\[V = \frac { 1} { 2} \left ( \frac { 4} { 3} \pi r^ 3 \right ) = \frac { 2} { 3} \pi r^ 3\]

3. Radius (r): The distance from the center to any point on the surface.

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