Question

A hemisphere is exactly​ one-half of a sphere. Find the volume of a hemisphere with radius​ = 10 m. Use pi almost equals 3.14 .

The volume of the hemisphere is

Answer 1

The volume \( V \) of a sphere is given by the formula:

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

To find the volume of a hemisphere, you simply take half of the volume of the sphere:

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

Given the radius \( r = 10 \, \text{m} \), we can substitute this value into the formula:

\[
V_{\text{hemisphere}} = \frac{2}{3} \pi (10)^3
\]

Calculating \( (10)^3 \):

\[
(10)^3 = 1000
\]

So:

\[
V_{\text{hemisphere}} = \frac{2}{3} \pi (1000) = \frac{2000}{3} \pi
\]

Now, substituting \( \pi \approx 3.14 \):

\[
V_{\text{hemisphere}} \approx \frac{2000}{3} \times 3.14
\]

Calculating \( \frac{2000}{3} \):

\[
\frac{2000}{3} \approx 666.67
\]

Now multiplying by \( 3.14 \):

\[
V_{\text{hemisphere}} \approx 666.67 \times 3.14 \approx 2093.34
\]

Thus, the volume of the hemisphere is approximately:

\[
\boxed{2093.34} \, \text{m}^3
\]