Question
David is a blacksmith who bought a solid sphere made of iron to melt down later and make hammers out of.
The volume of the sphere is cubic inches.
What is the radius of the sphere to the nearest tenth of an inch?
Use as an approximation for .
A
3.13.1 inches
B
2.62.6 inches
C
2.72.7 inches
D
4.14.1 inches
The volume of the sphere is cubic inches.
What is the radius of the sphere to the nearest tenth of an inch?
Use as an approximation for .
A
3.13.1 inches
B
2.62.6 inches
C
2.72.7 inches
D
4.14.1 inches
Answers
GPT-4o mini
To find the radius of the sphere given its volume, we use the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius. We can rearrange this formula to solve for the radius:
\[
r^3 = \frac{3V}{4\pi}
\]
\[
r = \left( \frac{3V}{4\pi} \right)^{1/3}
\]
Given that the volume \( V \) is provided (though not specified in your question), we'll continue with the formula, assuming you can substitute your specific volume.
For this calculation, let's assume \( V \) is known. Then we can use \( \pi \approx 3.14 \).
Plugging in \( \pi \):
\[
r = \left( \frac{3V}{4 \times 3.14} \right)^{1/3}
\]
To give a numerical answer, we'd need the value of \( V \). However, if you're simply looking for which of the multiple-choice answers corresponds to a specific volume, you would need to plug in the different volumes into the radius formula to calculate the radius corresponding to each option, or further clarify what volume you are working with.
Please provide the volume in cubic inches for a precise answer or follow the above method to calculate based on your volume.
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius. We can rearrange this formula to solve for the radius:
\[
r^3 = \frac{3V}{4\pi}
\]
\[
r = \left( \frac{3V}{4\pi} \right)^{1/3}
\]
Given that the volume \( V \) is provided (though not specified in your question), we'll continue with the formula, assuming you can substitute your specific volume.
For this calculation, let's assume \( V \) is known. Then we can use \( \pi \approx 3.14 \).
Plugging in \( \pi \):
\[
r = \left( \frac{3V}{4 \times 3.14} \right)^{1/3}
\]
To give a numerical answer, we'd need the value of \( V \). However, if you're simply looking for which of the multiple-choice answers corresponds to a specific volume, you would need to plug in the different volumes into the radius formula to calculate the radius corresponding to each option, or further clarify what volume you are working with.
Please provide the volume in cubic inches for a precise answer or follow the above method to calculate based on your volume.