Subjects geometry

Sphere Surface Area 189110

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Sphere Surface Area 189110


1. The problem asks to find the surface area $SA$ of a sphere given its volume $V=880$ ft$^3$. The formula for surface area is: $$SA = 4\pi \left(\frac{3V}{4\pi}\right)^{\frac{2}{3}}$$ 2. Here, $\pi$ is approximately 3.14, and $V$ is the volume. 3. Substitute $V=880$ and $\pi=3.14$ into the formula: $$SA = 4 \times 3.14 \times \left(\frac{3 \times 880}{4 \times 3.14}\right)^{\frac{2}{3}}$$ 4. Calculate inside the parentheses: $$\frac{3 \times 880}{4 \times 3.14} = \frac{2640}{12.56} \approx 210.19$$ 5. Raise 210.19 to the power $\frac{2}{3}$: $$210.19^{\frac{2}{3}} = \left(210.19^{\frac{1}{3}}\right)^2$$ 6. Find the cube root of 210.19: $$210.19^{\frac{1}{3}} \approx 5.95$$ 7. Square 5.95: $$5.95^2 = 35.40$$ 8. Multiply by $4 \times 3.14 = 12.56$: $$SA = 12.56 \times 35.40 = 444.62$$ 9. The approximate surface area is $444.62$ ft$^2$, which rounds to 444 ft$^2$. Final answer: approximately 444 ft$^2$ (Option B).