Question

The surface area of this cylinder is 347.2212 square inches.What is the height?
The radius is 5.7
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. 5.7 in h h ≈ inches

Answer 1

To find the height of the cylinder given the surface area and the radius, we can use the formula for the surface area \( A \) of a cylinder:

\[
A = 2\pi r(h + r)
\]

where:
- \( A \) is the surface area,
- \( r \) is the radius,
- \( h \) is the height.

We are given:
- \( A = 347.2212 \) square inches,
- \( r = 5.7 \) inches,
- and we can use \( \pi \approx 3.14 \).

First, we can substitute the values into the formula:

\[
347.2212 = 2 \times 3.14 \times 5.7 (h + 5.7)
\]

Now, calculate \( 2 \times 3.14 \times 5.7 \):

\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 5.7 = 35.706
\]

Now, we can rewrite the equation:

\[
347.2212 = 35.706(h + 5.7)
\]

Now divide both sides by \( 35.706 \):

\[
\frac{347.2212}{35.706} = h + 5.7
\]

Calculating the left side:

\[
\frac{347.2212}{35.706} \approx 9.73
\]

Now we can solve for \( h \):

\[
9.73 = h + 5.7
\]

Subtract \( 5.7 \) from both sides:

\[
h = 9.73 - 5.7
\]
\[
h \approx 4.03
\]

Thus, the height \( h \) of the cylinder is approximately \( \boxed{4.03} \) inches.