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 .
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 .
Answers
GPT-4o mini
To find the radius of a solid sphere given its volume, we can 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 want to solve for \( r \). First, we'll set up the equation with the volume you provided. Since you didn't specify the numerical value for \( V \), I will use \( V \) in the calculations.
1. Rearranging the formula to solve for \( r \):
\[
r^3 = \frac{3V}{4\pi}
\]
2. Now we substitute \( \pi \) with \( \frac{22}{7} \) (an approximation for \( \pi \)) and calculate \( r \):
\[
r^3 = \frac{3V}{4 \times \frac{22}{7}} = \frac{3V \times 7}{88} = \frac{21V}{88}
\]
3. To find \( r \), we take the cube root of both sides:
\[
r = \sqrt[3]{\frac{21V}{88}}
\]
4. Once you provide the volume \( V \) in cubic inches, we can plug it into this formula to find the radius \( r \).
Could you please provide the numerical value for the volume?
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius.
We want to solve for \( r \). First, we'll set up the equation with the volume you provided. Since you didn't specify the numerical value for \( V \), I will use \( V \) in the calculations.
1. Rearranging the formula to solve for \( r \):
\[
r^3 = \frac{3V}{4\pi}
\]
2. Now we substitute \( \pi \) with \( \frac{22}{7} \) (an approximation for \( \pi \)) and calculate \( r \):
\[
r^3 = \frac{3V}{4 \times \frac{22}{7}} = \frac{3V \times 7}{88} = \frac{21V}{88}
\]
3. To find \( r \), we take the cube root of both sides:
\[
r = \sqrt[3]{\frac{21V}{88}}
\]
4. Once you provide the volume \( V \) in cubic inches, we can plug it into this formula to find the radius \( r \).
Could you please provide the numerical value for the volume?