Question

a cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. a hole cut out of the center has a diameter of 6 millimeters. what is the volume of metal in the pipe? use 3.14 for π and round the answer to the nearest tenth of a cubic millimeter. 282.6 mm³ 271.3 mm³ 553.9 mm³ 836.5 mm³

Explanation:

Step1: Calculate outer - radius

The outer diameter is $d_{1}=8.4$ mm, so the outer - radius $r_{1}=\frac{d_{1}}{2}=\frac{8.4}{2}=4.2$ mm.

Step2: Calculate inner - radius

The inner diameter is $d_{2}=6$ mm, so the inner - radius $r_{2}=\frac{d_{2}}{2}=\frac{6}{2}=3$ mm.

Step3: Use the formula for the volume of a hollow cylinder

The volume formula for a hollow cylinder is $V=\pi h(r_{1}^{2}-r_{2}^{2})$, where $h = 10$ mm, $\pi=3.14$, $r_{1}=4.2$ mm and $r_{2}=3$ mm.
Substitute the values: $V = 3.14\times10\times(4.2^{2}-3^{2})$.
First, calculate $4.2^{2}-3^{2}=(4.2 + 3)(4.2 - 3)=(7.2)\times(1.2)=8.64$.
Then, $V=3.14\times10\times8.64$.
$V = 31.4\times8.64=271.296$ mm³.

Step4: Round the result

Rounding $271.296$ to the nearest tenth gives $271.3$ mm³.

Answer:

$271.3$ mm³