Question

a cylinder has a base diameter of 10 inches and a height of 17 inches. what is its volume in cubic inches, to the nearest tenths place?

Explanation:

Step1: Find the radius of the base

The diameter \( d = 10 \) inches, so the radius \( r=\frac{d}{2}=\frac{10}{2} = 5 \) inches.

Step2: Recall the formula for the volume of 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.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 5 \) inches and \( h=17 \) inches. So \( V=\pi\times(5)^{2}\times17=\pi\times25\times17 = 425\pi \).

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we get \( V\approx425\times3.14159\approx1335.17675 \).

Step5: Round to the nearest tenths place

Rounding \( 1335.17675 \) to the nearest tenths place gives \( 1335.2 \).

Answer:

\( 1335.2 \)