Question

select the correct answer.
for an art project, a cone is covered with paper without any gaps or overlaps. the height of the cone is 28 inches and its diameter is 14 inches.
what is the surface area of the covering to the nearest square inch?
a. 789 in²
b. 635 in²
c. 1,993 in²
d. 1,376 in²

Explanation:

Step1: Find the radius of the cone

The diameter of the cone is 14 inches, so the radius \( r=\frac{14}{2} = 7 \) inches.

Step2: Find the slant height \( l \) of the cone

Using the Pythagorean theorem for the cone (where height \( h = 28 \) inches, radius \( r = 7 \) inches), \( l=\sqrt{r^{2}+h^{2}}=\sqrt{7^{2}+28^{2}}=\sqrt{49 + 784}=\sqrt{833}\approx28.86 \) inches.

Step3: Calculate the surface area of the cone (lateral surface area + base area)

The formula for the lateral surface area of a cone is \( \pi rl \), and the base area is \( \pi r^{2} \). So total surface area \( S=\pi rl+\pi r^{2}=\pi r(l + r) \).
Substitute \( r = 7 \), \( l\approx28.86 \):
\( S=\pi\times7\times(28.86 + 7)=7\pi\times35.86\approx7\times3.14\times35.86\approx789 \) square inches.

Answer:

A. 789 in²