Question

What is the surface area of the cylinder with height 2 ft and radius 4 ft? Round your answer to the nearest thousandth.

Answer 1

Surface Area = 150.796 ft² (nearest thousandth)

Explanation:

Surface area of a cylinder

`\sf SA=2 \pi r^2+2 \pi rh`

where:

• r is the radius
• h is the height

Given:

• radius (r) = 4 ft
• height (h) = 2 ft

Substitute the given values into the formula and solve for SA:

`\begin{aligned}\sf SA & = \sf 2 \pi r^2 + 2 \pi rh\\\implies \sf SA & = \sf 2 \pi (4)^2 + 2 p\i (4)(2)\\& = \sf 2 \pi (16) + 2 \pi (8)\\& = \sf 32 \pi + 16 \pi \\& = \sf 48 \pi \\& = \sf 150.7964474... \\& = \sf 150.796 \:ft^2\: (nearest\:thousandth)\end{aligned}`

Therefore, the surface area of the cylinder with height 2 ft and radius 4ft is 150.796 ft² (nearest thousandth).

Answer 2

Lateral surface area:

• A = 2πrh = 2*3.14*4*2 = 50.24 ft²

Total surface area:

• S = 2πrh + 2πr² = 50.24 + 2*3.14*4² = 150.72 ft²