Question

find the surface area and volume of the solid. round each measure to the nearest tenth, if necessary.
(image of a cylinder with radius 6 in. and height 13 in.)
a) surface area = 226π or about 709.9 in²
volume = 466π or about 1463.9 in³
b) surface area = 228π or about 716.3 in²
volume = 468π or about 1470.3 in³
c) surface area = 220π or about 691.1 in²
volume = 460π or about 1445.1 in³
d) surface area = 228 in²
volume = 468 in³

Explanation:

Step1: Recall Cylinder Formulas

The surface area \( S \) of a cylinder is \( S = 2\pi r^2 + 2\pi rh \), and the volume \( V \) is \( V=\pi r^2h \). Here, \( r = 6 \) in, \( h = 13 \) in.

Step2: Calculate Surface Area

Substitute \( r = 6 \), \( h = 13 \) into surface area formula:
\( S = 2\pi(6)^2 + 2\pi(6)(13) \)
\( = 2\pi(36) + 2\pi(78) \)
\( = 72\pi + 156\pi \)
\( = 228\pi \)
Approximate: \( 228 \times 3.1416 \approx 716.3 \) \( \text{in}^2 \).

Step3: Calculate Volume

Substitute \( r = 6 \), \( h = 13 \) into volume formula:
\( V=\pi(6)^2(13) \)
\( = \pi(36)(13) \)
\( = 468\pi \)
Approximate: \( 468 \times 3.1416 \approx 1470.3 \) \( \text{in}^3 \).

Answer:

B) Surface area \( = 228\pi \) or about \( 716.3 \) \( \text{in}^2 \), Volume \( = 468\pi \) or about \( 1470.3 \) \( \text{in}^3 \)