Question

career math i unit 4 pre - test area, perimeter, and volume
a cylinder has a surface area of 1850 square yards and a radius of 9 yards.
calculate the volume of the cylinder and round your answer to the nearest tenth.
v = \\(\pi r^{2}h\\)
sa = 2\\(\pi r h+2\pi r^{2})
267.3\\(\pi\\) yd³
59.4\\(\pi\\) yd³
180\\(\pi\\) yd³
3.3\\(\pi\\) yd³

Explanation:

Step1: Substitute values into surface - area formula

Given $SA = 1850$, $r = 9$, and $SA=2\pi rh + 2\pi r^{2}$.
$1850=2\pi\times9\times h+2\pi\times9^{2}$
$1850 = 18\pi h+162\pi$

Step2: Solve for $h$

First, subtract $162\pi$ from both sides.
$1850 - 162\pi=18\pi h$
$1850-162\times3.14 = 18\times3.14\times h$
$1850 - 508.68=56.52h$
$1341.32 = 56.52h$
$h=\frac{1341.32}{56.52}\approx23.73$

Step3: Calculate the volume

Use the volume formula $V=\pi r^{2}h$ with $r = 9$ and $h\approx23.73$.
$V=\pi\times9^{2}\times23.73$
$V = 81\pi\times23.73$
$V\approx1922.13\pi\approx267.3\pi$ (rounded to the nearest tenth in terms of $\pi$)

Answer:

$267.3\pi$ yd³