Question

the volume of this cylinder is 9,074.6 cubic centimeters. what is the height? use π ≈ 3.14 and round your answer to the nearest hundredth. 17 cm h h ≈ □ centimeters submit

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 9074.6 \) cubic centimeters, \( \pi \approx 3.14 \), and \( r = 17 \) centimeters. We need to solve for \( h \).

First, we can rearrange the formula to solve for \( h \): \( h=\frac{V}{\pi r^2} \)

Step2: Calculate \( r^2 \)

\( r = 17 \), so \( r^2=17^2 = 289 \)

Step3: Calculate \( \pi r^2 \)

Substitute \( \pi = 3.14 \) and \( r^2 = 289 \) into \( \pi r^2 \):
\( \pi r^2=3.14\times289 = 3.14\times200+3.14\times80 + 3.14\times9=628+251.2 + 28.26=907.46 \)

Step4: Solve for \( h \)

Now, substitute \( V = 9074.6 \) and \( \pi r^2=907.46 \) into the formula for \( h \):
\( h=\frac{9074.6}{907.46}=10.00 \) (since \( 9074.6\div907.46 = 10 \))

Answer:

\( 10.00 \)