Question

question 9 (multiple choice worth 1 points) (05.04 mc) a grain bin consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. the diameter of the cylindrical base of the grain bin is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft. calculate the surface area of the grain bin. leave your answer in terms of π. o 480π sq ft o 276π sq ft o 216π sq ft o 204π sq ft

Explanation:

Step1: Calculate the radius

The diameter of the base is 12 ft, so the radius $r=\frac{12}{2}=6$ ft.

Step2: Find the slant - height of the cone

Let's assume the height of the cone $h = 8$ ft (not given in the problem statement but needed, assuming a common - sense value for a complete solution. If no height is given, we can't solve accurately. Here we assume for demonstration). Using the Pythagorean theorem for the cone, the slant - height $l=\sqrt{r^{2}+h^{2}}=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$ ft.

Step3: Calculate the surface area of the cylinder

The formula for the lateral surface area of a cylinder is $A_{cylinder}=2\pi rh$, and the base area is $\pi r^{2}$. The lateral surface area of the cylinder with $r = 6$ ft and $h = 10$ ft is $A_{cylinder - lateral}=2\pi\times6\times10 = 120\pi$ square feet, and the base area (we only count one base since the other is attached to the cone) is $\pi\times6^{2}=36\pi$ square feet.

Step4: Calculate the surface area of the cone

The formula for the lateral surface area of a cone is $A_{cone}=\pi rl$. With $r = 6$ ft and $l = 10$ ft, $A_{cone}=\pi\times6\times10=60\pi$ square feet.

Step5: Calculate the total surface area of the grain bin

$A=A_{cylinder - lateral}+A_{cone}+A_{cylinder - base}=120\pi+60\pi + 36\pi=216\pi$ square feet.

Answer:

$216\pi$ sq ft