What is the radius of a sphere with a volume of $802 \mathrm{~m}^{3}$, to the nearest tenth of a meter?

Step 1 ：Given the volume of the sphere, \(V = 802 \mathrm{~m}^{3}\)

Step 2 ：Use the formula for the volume of a sphere, \(V = \frac{4}{3} \pi r^3\)

Step 3 ：Rearrange the formula to isolate r: \(r^3 = \frac{3V}{4\pi}\)

Step 4 ：Take the cube root of both sides to solve for r: \(r = \sqrt[3]{\frac{3V}{4\pi}}\)

Step 5 ：Plug in the given volume (802 m³) and calculate the radius: \(r = \sqrt[3]{\frac{3(802)}{4\pi}}\)

Step 6 ：Calculate the radius: \(r \approx 5.763618849184167\)

Step 7 ：Round the radius to the nearest tenth of a meter: \(r \approx 5.8\)

Step 8 ：\(\boxed{\text{The radius of the sphere with a volume of 802 m³ is approximately 5.8 meters}}\)