Question

A sphere has a volume of 850 m^3 find its surface area

Answer 1

Answer:

SA ≈ 434.5 cm²

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = $\frac{4}{3}$πr³ ( r is the radius )

The surface area (SA) is calculated as

SA = 4πr²

To find r use the volume formula

$\frac{4}{3}$πr³ = 850 ( multiply both sides by $\frac{3}{4}$ to clear the fraction )

πr³ = 637.5 ( divide both sides by π )

r³ = $\frac{637.5}{\pi }$ ( take the cube root of both sides )

r = $\sqrt[3]{\frac{637.5}{\pi } }$ ≈ 5.88 cm ( to 2 dec. places )

Then

SA = 4π × 5.88² ≈ 434.5 cm² ( to 1 dec. place )