Question

A right circular cylinder has a base whose area is 154 square feet. If the height of the cylinder is 19 feet, what is its lateral surface area? Use π = 22/7

Answer 1

lateral surface area= h* 22/7*2*r

Answer 2

base area = 22/7*2*r
154=22/7*2*r
154=44/7*r
154*7=44r
(154*7)/44=r

Answer 3

r = 24.5
LA = 19 * 22/7 * 2 * 24.5
LA = 2926?

but it isn't one of my answer choices

Answer 4

my answer choices are;
836 ft^2
990 ft^2
1672 ft^2
1980 ft^2
i tried solving it different ways before but it never ended up with the answer

Answer 5

hold on

Answer 6

Base is a circle, so \(A_c = \pi r^2 \). We know that \(A_c = 154\). We want to find the circumference because the Lateral Surface Area is \(2 \pi r h\), the circumference of the circle times the height (since if we cut the cylinder down the side vertically and unrolled it, it'd become a rectangle with base as circumference and height stays the same).
\[\begin{align}
A_c = A_c \implies \pi r^2 &= 154\qquad \pi \approx \frac{22}{7} \\
\frac{22}{7}r^2 & = 154 \\
\end{align}
\]

Answer 7

so the radius will equal 7; which would fit, since 2 * 22/7 * 7 * 19 = 836 ft^2.

Answer 8

Yes. :)

Answer 9

thanks alot , i was really stuck not getting what to do ☺

Answer 10

You're welcome. :)
I had a few issues myself (I kept trying to use r=49, which led to strangely large results... lol)