what’s the radius of a globe that has a volume of 904.78 in^4?

1 answer

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.