Question

unit exam: three - dimensional figures
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a graduated cylinder in a lab has a radius of 3.9 centimeters and a height of 11.7 centimeters. the cylinder is used to store a liquid chemical. what is the maximum volume of the chemical that the cylinder can hold? use 3.14 for π. round your answer to the nearest tenth at the end of the calculation.
use the keypad to type your answer in the box provided.
the maximum volume of the chemical the cylinder can hold is □ cubic centimeters.

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

Given \(r = 3.9\) cm, \(h=11.7\) cm, and \(\pi = 3.14\).
First, calculate \(r^{2}\): \(r^{2}=(3.9)^{2}=3.9\times3.9 = 15.21\).
Then, substitute into the formula: \(V=3.14\times15.21\times11.7\).
Calculate \(3.14\times15.21\): \(3.14\times15.21=(3 + 0.14)\times15.21=3\times15.21+0.14\times15.21=45.63+2.1294 = 47.7594\).
Now, calculate \(47.7594\times11.7\): \(47.7594\times11.7=(47+0.7594)\times11.7=47\times11.7+0.7594\times11.7\).
\(47\times11.7=(50 - 3)\times11.7=50\times11.7-3\times11.7=585 - 35.1 = 549.9\).
\(0.7594\times11.7=(0.7+0.05+0.0094)\times11.7=0.7\times11.7+0.05\times11.7+0.0094\times11.7=8.19+0.585 + 0.10998=8.88498\).
\(47.7594\times11.7=549.9+8.88498 = 558.78498\).

Answer:

\(558.8\)