Question

the volume of the oblique cylinder is 5,588 mm³. if the radius is 11 mm, what is the height? round the answer to the nearest tenth of a millimeter. 3.8 mm 3.8 mm³ 14.7 mm 14.7 mm³

Explanation:

Step1: Recall the volume formula for a cylinder (oblique or right, volume is same)

The volume \( V \) of a cylinder is given by \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We need to solve for \( h \), so rearrange the formula: \( h = \frac{V}{\pi r^{2}} \)

Step2: Substitute the given values

We know \( V = 5588 \, \text{mm}^3 \) and \( r = 11 \, \text{mm} \). Plug these into the formula:
First, calculate \( r^{2}=11^{2} = 121 \)
Then, \( \pi r^{2}=\pi\times121\approx3.1416\times121\approx380.1326 \)
Now, \( h=\frac{5588}{380.1326}\approx14.7 \) (rounded to the nearest tenth)

Also, note that height is a length, so the unit is mm (not \( \text{mm}^3 \), which is volume), so we eliminate options with \( \text{mm}^3 \). The value we calculated is approximately 14.7 mm.

Answer:

14.7 mm