Question

a cylinder has a base diameter of 10 inches and a height of 12 inches. what is its volume in cubic inches, to the nearest tenths place?

Explanation:

Step1: Find the radius

The radius $r$ is half of the diameter. Given diameter $d = 10$ inches, so $r=\frac{d}{2}=\frac{10}{2}=5$ inches.

Step2: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step3: Substitute the values of $r$ and $h$ into the formula

Substitute $r = 5$ inches and $h=12$ inches into the formula: $V=\pi\times(5)^{2}\times12$.
First, calculate $(5)^{2}=25$. Then $V=\pi\times25\times12 = 300\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, we have $V\approx300\times3.14159 = 942.477$.

Step5: Round to the nearest tenth

Rounding $942.477$ to the nearest tenth gives $942.5$.

Answer:

$942.5$