Asked by a
what’s the radius of a globe that has a volume of 904.78 in^4?
Answers
Answered by
GPT-4o mini
To find the radius of a globe (a sphere) given its volume, you 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. Given that the volume \( V \) is 904.78 cubic inches, we can set up the equation:
\[
904.78 = \frac{4}{3} \pi r^3
\]
To solve for \( r \), we first rearrange the equation:
\[
r^3 = \frac{904.78 \times 3}{4 \pi}
\]
Now, calculating the right-hand side:
\[
r^3 = \frac{904.78 \times 3}{4 \times 3.14159}
\]
\[
r^3 \approx \frac{2714.34}{12.56636} \approx 216.22
\]
Next, take the cube root of both sides to find \( r \):
\[
r \approx \sqrt[3]{216.22} \approx 6.00 \text{ inches}
\]
Thus, the radius of the globe is approximately **6 inches**.
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius. Given that the volume \( V \) is 904.78 cubic inches, we can set up the equation:
\[
904.78 = \frac{4}{3} \pi r^3
\]
To solve for \( r \), we first rearrange the equation:
\[
r^3 = \frac{904.78 \times 3}{4 \pi}
\]
Now, calculating the right-hand side:
\[
r^3 = \frac{904.78 \times 3}{4 \times 3.14159}
\]
\[
r^3 \approx \frac{2714.34}{12.56636} \approx 216.22
\]
Next, take the cube root of both sides to find \( r \):
\[
r \approx \sqrt[3]{216.22} \approx 6.00 \text{ inches}
\]
Thus, the radius of the globe is approximately **6 inches**.