Question

A silo is constructed using a cylinder with a hemisphere on top. The circumference of the hemisphere and the circumference of the cylinder are equal. The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall. One of the circular bases on the cylinder is in contact with the ground. What is the area of the surface of the silo that will be exposed to rain, wind, and sun?

Answer 1

A) 450

Explanation:

I just took the test

Answer 2

1. The surface that will be exposed to the rain is the lateral surface of the cylinder and the hemisphere.

2. The lateral area of the cylinder is a rectangle with height equal to the height of the cylinder and width equal to the circumference of the base of the cylinder.

3. the circumference of the base = 2
`\pi`r=2*
`\pi`*5=10
`\pi`
so the lateral area = 10
`\pi`*h=10
`\pi`*40=400
`\pi` (
`ft^(2)`)

4. The surface area of a sphere is
`4 \pi r^(2)`
so the surface of the hemisphere =
`(1)/(2) *4 \pi r^(2)=2 \pi (5)^(2)=50 \pi`(
`ft^(2)`)

5. Total area exposed = 450
`\pi`
`ft^(2)`