Question

a cylinder has a diameter of 14 centimeters and a volume of 1000 cubic centimeters. what is its height? express your answer to the nearest tenth of a centimeter.

Explanation:

Step1: Find the radius of the cylinder

The diameter \( d = 14 \) cm, so the radius \( r=\frac{d}{2}=\frac{14}{2} = 7 \) cm.

Step2: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by \( V=\pi r^{2}h \), where \( h \) is the height. We know \( V = 1000 \) \( cm^{3}\) and \( r = 7 \) cm. We need to solve for \( h \). Rearranging the formula for \( h \), we get \( h=\frac{V}{\pi r^{2}} \).

Step3: Substitute the values into the formula

Substitute \( V = 1000 \), \( r=7 \) into the formula: \( h=\frac{1000}{\pi\times(7)^{2}}=\frac{1000}{\pi\times49}\).

Step4: Calculate the value of \( h \)

First, calculate \( \pi\times49\approx3.1416\times49 = 153.9384 \). Then, \( h=\frac{1000}{153.9384}\approx6.5 \) (rounded to the nearest tenth).

Answer:

\( 6.5 \)