Question

Compare the volume and surface area of a sphere with diameter 5 ft with that of a cylinder with height 2 ft and a base with radius 3 ft.​

Answer 1

Sphere Volume= 65.45 cubic feet
Cylinder Volume = 56.55 cubic feet

Sphere Area = 78.54 square feet

Cylinder Area = 94.25 square feet

Explanation:

Here are the equations for the volume and surface area of a sphere with radius r and a cylinder with radius r and height .

Sphere Cylinder

Volume V = (4/3)πr³ V = πr²h

Surface Area A = 4πr² A = 2πr(h + r)

For a sphere with diameter 5 feet (r = 5/2 = 2.5 feet)

`V = (4)/(3)\pi r^3 = (4)/(3) (2.5)^3\pi = 20.8333\pi = 65.45 \text{ cubic feet}\\`

`A = 4\pi r^2 = 4 \pi (2.5)^2 = 25\pi = 78.54 \text{ square feet}`

For a cylinder with r = 3 feet and h= 2 feet,

`V = \pi r^2h = \pi (3)^2\cdot 2 = 18\pi = 56.55 \text{ cubic feet}`

`A = 2\pi r(h + r) = 2\pi\cdot 3 (2 + 3) = 6\pi (5)= 30\pi =94.25 \text { square feet}`