Question

the surface area of this cylinder is 922.4064 square yards what is the height use pi = 3.14 and round you're answer to the nearest hundredth the radius is 9.6yd and height is h

Answer 1

To find the height of the cylinder, we can use the formula for the surface area of a cylinder, which is given by:

\[
SA = 2\pi r^2 + 2\pi rh
\]

where \(SA\) is the surface area, \(r\) is the radius, and \(h\) is the height.

From the problem, we know:
- \(SA = 922.4064\) square yards
- \(r = 9.6\) yards
- \(\pi \approx 3.14\)

First, let's calculate \(2\pi r^2\):

\[
2\pi r^2 = 2 \times 3.14 \times (9.6)^2
\]

Calculating \( (9.6)^2 \):

\[
(9.6)^2 = 92.16
\]

Now plug this back into the surface area equation:

\[
2\pi r^2 = 2 \times 3.14 \times 92.16 = 577.8384 \text{ square yards}
\]

Now, we substitute \(2\pi r^2\) back into the surface area equation:

\[
922.4064 = 577.8384 + 2\pi rh
\]

Now, isolate \(2\pi rh\):

\[
2\pi rh = 922.4064 - 577.8384 = 344.568
\]

Substituting for \(2\pi\) and \(r\):

\[
2\pi rh = 2 \times 3.14 \times 9.6 \times h
\]
\[
344.568 = 2 \times 3.14 \times 9.6 \times h
\]

Calculating \(2 \times 3.14 \times 9.6\):

\[
2 \times 3.14 \times 9.6 = 60.096
\]

Thus, we have:

\[
344.568 = 60.096h
\]

Now, solving for \(h\):

\[
h = \frac{344.568}{60.096} \approx 5.735
\]

Now rounding to the nearest hundredth:

\[
h \approx 5.74
\]

So, the height of the cylinder is approximately **5.74 yards**.