Question

What is the volume of a sphere with a radius of 5.5 kilometers, estimated to the hundredths place using 3.14 for π?

Answer 1

To calculate the volume of a sphere, we use the formula:

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

where \( V \) is the volume and \( r \) is the radius.

Given that the radius \( r \) is 5.5 kilometers and using \( \pi \approx 3.14 \), we can substitute the values into the formula.

First, we calculate \( r^3 \):

\[
r^3 = (5.5)^3 = 5.5 \times 5.5 \times 5.5
\]

Calculating step by step:

\[
5.5 \times 5.5 = 30.25
\]

Now, multiplying by 5.5 again:

\[
30.25 \times 5.5 = 166.375
\]

So, \( r^3 \approx 166.375 \).

Now we can plug this back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 166.375
\]

Calculating \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.18666667
\]

Now multiply by \( 166.375 \):

\[
V \approx 4.18666667 \times 166.375 \approx 696.3608333
\]

Rounding this to the hundredths place, we get:

\[
V \approx 696.36 \text{ cubic kilometers}
\]

Thus, the volume of the sphere is approximately **696.36 cubic kilometers**.