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? \bigcirc 450\pi square feet \bigcirc 475\pi square feet \bigcirc 500\pi square feet \bigcirc 525\pi square feet

Explanation:

Step1: Find cylinder radius

The diameter of the cylinder is 10 ft, so radius $r = \frac{10}{2} = 5$ ft.

Step2: Calculate cylinder lateral surface area

Lateral surface area of cylinder is $2\pi rh$. Here $h=40$ ft:
$2\pi \times 5 \times 40 = 400\pi$ square feet

Step3: Calculate hemisphere surface area

Curved surface area of hemisphere is $2\pi r^2$ (we exclude the flat face since it's attached to the cylinder):
$2\pi \times 5^2 = 2\pi \times 25 = 50\pi$ square feet

Step4: Sum exposed areas

Add cylinder lateral area and hemisphere curved area:
$400\pi + 50\pi = 450\pi$ square feet

Answer:

450π square feet