Question

1. find the volume of the cylinder. round to the nearest hundredth. 12.7 in 8.4 in type a response

Explanation:

Step1: 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 of the base and \( h \) is the height (or length) of the cylinder.

Step2: Determine the radius and height

From the diagram, the diameter of the base is \( 8.4 \) in, so the radius \( r=\frac{8.4}{2}=4.2 \) in. The height (length) of the cylinder \( h = 12.7 \) in (assuming the "127 in" is a typo and should be "12.7 in", otherwise the number would be too large, we proceed with 12.7 in for a reasonable calculation).

Step3: Substitute the values into the formula

\( V=\pi\times(4.2)^{2}\times12.7 \)

First, calculate \( (4.2)^{2}=4.2\times4.2 = 17.64 \)

Then, \( 17.64\times12.7=17.64\times(12 + 0.7)=17.64\times12+17.64\times0.7=211.68+12.348 = 224.028 \)

Then, \( V=\pi\times224.028\approx3.14159\times224.028\approx703.46 \) (if we use \( \pi\approx3.14159 \))

If we assume the height is 127 in (as per the original typo), then:

\( (4.2)^{2}=17.64 \)

\( 17.64\times127 = 17.64\times(100 + 20+7)=1764+352.8 + 123.48=2240.28 \)

\( V=\pi\times2240.28\approx3.14159\times2240.28\approx7034.6 \)

But since 127 in height with 8.4 in diameter is an unusually large cylinder, we assume the height is 12.7 in (a decimal point typo). So we proceed with \( h = 12.7 \) in.

Answer:

If \( h = 12.7 \) in, the volume is approximately \( 703.46 \) cubic inches. If \( h=127 \) in, the volume is approximately \( 7034.6 \) cubic inches. (We assume the height is \( 12.7 \) in due to the context of "nearest hundredth" and reasonable size, so the answer is approximately \( 703.46 \) in³)