Question

The surface area of a cylinder is given by the formula SA = 2Xr^2 + 2Xrh.

A cylinder has a radius of 13 cm and a surface area of 1,430X cm^2 .

Find the height of the cylinder. X=pi
40 cm
28 cm
42 cm
51 cm

Answer 1

@kirbykirby

Answer 2

\(SA=2\pi r^2 +2\pi r h\\
1430 = 2\pi (13)^2+2\pi(13)h\\
1430=2\pi(169)+26\pi h\\
1430=338\pi +26\pi h\)

do you know how to solve the rest?

Answer 3

No

Answer 4

\(1430=338\pi +26\pi h\)

subtract \(338\pi\) from both sides:

\(1430 - 338 \pi = 338 \pi + 26\pi h - 338 \pi\\
1430-338\pi=26\pi h\)

So isolate h, divide by \(26 \pi\) on both sides.:

\[\frac{1430-338\pi}{26\pi}=\frac{26\pi h}{26\pi}\\
~ \\
\frac{1430-338 \pi}{26\pi}=h \]

Answer 5

If you want you could simplify this a bit more:

\[\h=frac{1430-338 \pi}{26\pi}=\frac{1430}{26\pi}-\frac{338\pi}{26\pi}=\frac{55}{\pi}-13

Answer 6

\[ h=\frac{1430-338 \pi}{26\pi}=\frac{1430}{26\pi}-\frac{338\pi}{26\pi}=\frac{55}{\pi}-13\]

Answer 7

oh I see what happened, the surface area was \(1430 \pi\) ... not just 1430. You can just follow the same steps above but just attach \(pi\) next to 1430. You should get \(h = 55-13 = 42\)