Question

Aimee packs ice cream into a cone then puts a hemisphere of ic cream on top of the cone that has a diameter of 5
What is the volume of the hemisphere rounded to the nearest hundredth use 3.14 for pi

Answer 1

To find the volume of the hemisphere of ice cream, we can use the formula for the volume of a hemisphere:

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

Where \( r \) is the radius of the hemisphere.

Given that the diameter of the hemisphere is 5, we can find the radius:

\[
r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5
\]

Now, we can substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):

\[
V = \frac{2}{3} \times 3.14 \times (2.5)^3
\]

Calculating \( (2.5)^3 \):

\[
(2.5)^3 = 15.625
\]

Now, substitute this value back into the volume formula:

\[
V = \frac{2}{3} \times 3.14 \times 15.625
\]

Calculating the multiplication:

\[
3.14 \times 15.625 = 49.0625
\]

Now, applying the \(\frac{2}{3}\):

\[
V = \frac{2}{3} \times 49.0625 = \frac{98.125}{3} \approx 32.7083
\]

Finally, rounding to the nearest hundredth, the volume is:

\[
\text{Volume} \approx 32.71
\]

Thus, the volume of the hemisphere is approximately **32.71 cubic units**.