Question

calculate the volume of a sphere with a diameter of 13 mm

Answer 1

To calculate the volume of a sphere, you can use the formula:

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

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

First, find the radius by dividing the diameter by 2. Given that the diameter is 13 mm:

\[
r = \frac{13 \text{ mm}}{2} = 6.5 \text{ mm}
\]

Now, substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (6.5 \text{ mm})^3
\]

Calculating \( (6.5)^3 \):

\[
(6.5)^3 = 6.5 \times 6.5 \times 6.5 = 274.625 \text{ mm}^3
\]

Now substitute this value back into the volume formula:

\[
V = \frac{4}{3} \pi (274.625 \text{ mm}^3)
\]

Calculating \( \frac{4}{3} \times 274.625 \):

\[
\frac{4}{3} \times 274.625 \approx 365.8333 \text{ mm}^3
\]

Now multiplying this by \( \pi \) (approximately 3.14159):

\[
V \approx 365.8333 \times 3.14159 \approx 1147.227 \text{ mm}^3
\]

Thus, the volume of the sphere is approximately:

\[
V \approx 1147.23 \text{ mm}^3
\]