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: Find outer radius

Outer diameter = 8.4 mm, so outer radius $r_o = \frac{8.4}{2} = 4.2$ mm

Step2: Find inner radius

Inner diameter = 6 mm, so inner radius $r_i = \frac{6}{2} = 3$ mm

Step3: Calculate outer cylinder volume

Use $V_o = \pi r_o^2 h$. Substitute values:
$V_o = 3.14 \times (4.2)^2 \times 10 = 3.14 \times 17.64 \times 10 = 553.896$ mm³

Step4: Calculate inner cylinder volume

Use $V_i = \pi r_i^2 h$. Substitute values:
$V_i = 3.14 \times (3)^2 \times 10 = 3.14 \times 9 \times 10 = 282.6$ mm³

Step5: Subtract volumes for metal volume

Metal volume $V = V_o - V_i$
$V = 553.896 - 282.6 = 271.296$ mm³

Step6: Round to nearest tenth

$271.296 \approx 271.3$ mm³

Answer:

271.3 mm³