Question

find the surface area of each figure. complete parts (a) through (e) below
the surface area of the sphere is 196π cm²
(simplify your answer. type an exact answer, using radicals as needed. type an exact answer, using π as needed.)
e. right circular cone
the surface area of the right circular cone is
(simplify your answer. type an exact answer, using radicals as needed. type an exact answer, using π as needed.)

Explanation:

Step1: Find the slant height \( l \)

Use the Pythagorean theorem \( l=\sqrt{r^{2}+h^{2}} \). Given \( r = 12\mathrm{cm}\) and \( h=16\mathrm{cm}\), then \( l=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20\mathrm{cm}\)

Step2: Calculate the surface area \( S \)

The surface area formula for a cone is \( S=\pi r(r + l)\). Substitute \( r = 12\mathrm{cm}\) and \( l = 20\mathrm{cm}\) into the formula: \( S=\pi\times12\times(12 + 20)=12\pi\times32 = 384\pi\mathrm{cm}^{2}\)

Answer:

\(384\pi\)