Question

chapter 8 practice: volume and capacity of cones, pyramids, and spheres
do the following questions on your own first and then check your answers in the appendix.
lesson 1: drilling for understanding

1. find the volume to the nearest cubic inch of a cone with a radius of 3 inches and a height of 8 inches.

we know
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Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Substitute values

Given $r = 3$ inches and $h=8$ inches. Substitute into the formula: $V=\frac{1}{3}\pi\times(3)^{2}\times8$.

Step3: Simplify the expression

First, $(3)^{2}=9$. Then $V=\frac{1}{3}\pi\times9\times8$. $\frac{1}{3}\times9 = 3$, so $V = 3\pi\times8=24\pi$.

Step4: Approximate the value

Taking $\pi\approx3.14$, we have $V\approx24\times3.14 = 75.36$. Rounding to the nearest cubic - inch, $V\approx75$ cubic inches.

Answer:

75 cubic inches