What is the radius of a sphere with a volume of \( 7961 \mathrm{~cm}^{3} \), to the nearest tenth of a centimeter?

To find the radius of a sphere given its volume, you can use the formula for the volume of a sphere, which is \( V = \frac{4}{3} \pi r^3 \). Rearranging this to solve for the radius \( r \), we have: \[ r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}} \] Plugging in the volume \( V = 7961 \mathrm{~cm}^3 \): \[ r = \left(\frac{3 \times 7961}{4 \pi}\right)^{\frac{1}{3}} \approx \left(\frac{23883}{12.5664}\right)^{\frac{1}{3}} \approx \left(1905.23\right)^{\frac{1}{3}} \approx 12.5 \mathrm{~cm} \] So, the radius of the sphere is approximately \( 12.5 \mathrm{~cm} \) when rounded to the nearest tenth of a centimeter. The quest for understanding volumes extends beyond just math classes; architects and engineers use these formulas to calculate materials needed for curved surfaces in buildings and structures. Just imagine the marvel of a dome-shaped roof and the precision required to ensure structural stability! Don’t forget about unit conversions! If you ever need to transition between metric units like centimeters to meters, remember that 1 meter equals 100 centimeters. This is crucial in practical applications like crafting or engineering, ensuring calculations remain consistent across larger scales!