Question
Find the volume of the sphere.
8 mm
The radius of the sphere is ___. When I find the volume of the sphere the answer is ___.
8 mm
The radius of the sphere is ___. When I find the volume of the sphere the answer is ___.
Answers
GPT-4o mini
To find 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.
Given that the diameter of the sphere is 8 mm, the radius \( r \) can be calculated as:
\[
r = \frac{\text{diameter}}{2} = \frac{8 \text{ mm}}{2} = 4 \text{ mm}
\]
Now, substituting the radius into the volume formula:
\[
V = \frac{4}{3} \pi (4 \text{ mm})^3
\]
Calculating \( (4 \text{ mm})^3 \):
\[
(4 \text{ mm})^3 = 64 \text{ mm}^3
\]
Now plug this into the volume formula:
\[
V = \frac{4}{3} \pi \times 64 \text{ mm}^3
\]
\[
V = \frac{256}{3} \pi \text{ mm}^3
\]
To get a numerical value, we can approximate \( \pi \) as 3.14:
\[
V \approx \frac{256}{3} \times 3.14 \approx 268.08 \text{ mm}^3
\]
So, to summarize:
The radius of the sphere is **4 mm**. When I find the volume of the sphere, the answer is approximately **268.08 mm³** (or precisely **\(\frac{256}{3} \pi \text{ mm}^3\)**).
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 8 mm, the radius \( r \) can be calculated as:
\[
r = \frac{\text{diameter}}{2} = \frac{8 \text{ mm}}{2} = 4 \text{ mm}
\]
Now, substituting the radius into the volume formula:
\[
V = \frac{4}{3} \pi (4 \text{ mm})^3
\]
Calculating \( (4 \text{ mm})^3 \):
\[
(4 \text{ mm})^3 = 64 \text{ mm}^3
\]
Now plug this into the volume formula:
\[
V = \frac{4}{3} \pi \times 64 \text{ mm}^3
\]
\[
V = \frac{256}{3} \pi \text{ mm}^3
\]
To get a numerical value, we can approximate \( \pi \) as 3.14:
\[
V \approx \frac{256}{3} \times 3.14 \approx 268.08 \text{ mm}^3
\]
So, to summarize:
The radius of the sphere is **4 mm**. When I find the volume of the sphere, the answer is approximately **268.08 mm³** (or precisely **\(\frac{256}{3} \pi \text{ mm}^3\)**).