(Types of Area MC)
A cone has a slant height of 8 inches and a diameter of 10 inches. What is the surface area of the cone?
65 in $^{2}$
$65 \pi$ in $^{2}$
$180 \mathrm{in}^{2}$
$180 \pi$ in $^{2}$
Answer
\(\boxed{A = 65\pi}\) square inches is the surface area of the cone.
Step 1 ：Given that the diameter of the cone is 10 inches, we can find the radius r which is half of the diameter. So, \(r = \frac{10}{2} = 5\) inches.
Step 2 ：The slant height l is given as 8 inches.
Step 3 ：The surface area A of a cone is given by the formula \(A = \pi r(r + l)\).
Step 4 ：Substitute the values of r and l into the formula: \(A = \pi * 5 * (5 + 8)\).
Step 5 ：Simplify the expression to find the surface area: \(A = \pi * 5 * 13 = 65\pi\) square inches.
Step 6 ：\(\boxed{A = 65\pi}\) square inches is the surface area of the cone.
