Question

What is the largest volume a sphere can have if it is covered by 6m2 of fabric?

Answer 1

The formula for determining the surface area of a sphere is expressed as

Surface area = 4 * pi * radius^2

From the information given,

surface area = 6

pi = 3.14

thus,

6 = 4 * 3.14 * radius^2

6 = 12.56radius^2

`\begin{gathered} radius^2\text{ = }(6)/(12.56)=0.478 \\ \text{radius = }\sqrt[]{0.478} \\ \text{radius = 0.69} \end{gathered}`

The formula for determining the volume of a sphere is expressed as

Volume = 4/3 * pi * radius^3

Thus,

Volume of sphere = 4/3 * 3.14 * 0.69^3

Volume of sphere = 1.38m^3