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? 450π square feet 475π square feet 500π square feet 525π square feet

Explanation:

Step1: Find the radius of the cylinder and hemisphere

The diameter of the circular - base of the cylinder $d = 10$ feet, so the radius $r=\frac{d}{2}=5$ feet. Since the circumference of the hemisphere and the cylinder are equal, they have the same radius $r = 5$ feet.

Step2: Calculate the lateral surface area of the cylinder

The formula for the lateral surface area of a cylinder is $A_{l - cylinder}=2\pi rh$. Here, $r = 5$ feet and $h = 40$ feet. So $A_{l - cylinder}=2\pi\times5\times40=400\pi$ square feet.

Step3: Calculate the surface area of the hemisphere

The formula for the surface area of a hemisphere is $A_{hemisphere}=2\pi r^{2}$. Substituting $r = 5$ feet, we get $A_{hemisphere}=2\pi\times5^{2}=50\pi$ square feet.

Step4: Calculate the area of the top - circular face of the cylinder

The formula for the area of a circle is $A_{circle}=\pi r^{2}$. Substituting $r = 5$ feet, we get $A_{circle}=\pi\times5^{2}=25\pi$ square feet.

Step5: Calculate the total exposed surface area

The total exposed surface area $A=A_{l - cylinder}+A_{hemisphere}+A_{circle}=400\pi+50\pi + 25\pi=475\pi$ square feet.

Answer:

B. $475\pi$ square feet