Question

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

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 6$ in and $h=13$ in.
$S=2\pi(6)^{2}+2\pi(6)(13)$

Step2: Calculate each term

First term: $2\pi(6)^{2}=2\pi\times36 = 72\pi$. Second term: $2\pi(6)(13)=156\pi$. Then $S=72\pi + 156\pi=228\pi\approx228\times3.14 = 716.3$ in².

Step3: Recall volume formula

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r = 6$ in and $h = 13$ in.
$V=\pi(6)^{2}(13)$

Step4: Calculate volume

$V=\pi\times36\times13 = 468\pi\approx468\times3.14=1470.3$ in³

Answer:

B. Surface area = 228π or about 716.3 in², Volume = 468π or about 1470.3 in³