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What is the volume, in cubic feet, of a cylinder with a height of 17 feet and a base radius of 8 feet, to the nearest tenths place?
Answer:
V=◻ feet
^(3)

What is the volume, in cubic feet, of a cylinder with a height of $17$ feet and a base radius of $8$ feet, to the nearest tenths place? $\newline$ Answer: $V=\square$ feet $^{3}$

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Convert between customary and metric systems

Full solution

Q. What is the volume, in cubic feet, of a cylinder with a height of

17

feet and a base radius of

8

feet, to the nearest tenths place?

\newline

Answer:

V=\square

feet

^{3}

Given Data: To find the volume of a cylinder, we use the formula $V = \pi r^2 h$ , where $V$ is the volume, $r$ is the radius of the base, and $h$ is the height of the cylinder. We are given the radius $r = 8$ feet and the height $h = 17$ feet.
Calculate Base Area: First, we calculate the area of the base of the cylinder, which is a circle. The area $A$ of a circle is given by the formula $A = \pi r^2$ . Substituting the given radius, we get $A = \pi(8 \text{ feet})^2$ .
Multiply Base Area and Height: Calculating the area of the base, we have $A = \pi(64 \text{ feet}^2) = 64\pi \text{ feet}^2$ .
Calculate Volume: Next, we multiply the area of the base by the height of the cylinder to find the volume. So, $V = 64\pi \text{ feet}^2 \times 17 \text{ feet}$ .
Approximate Volume with $\pi$ : Performing the multiplication, we get $V = 1088\pi$ cubic feet.
Calculate Approximate Volume: To express the volume to the nearest tenths place, we need to use the approximate value of $\pi$ , which is $3.1416$ . So, $V \approx 1088 \times 3.1416$ cubic feet.
Round to Nearest Tenth: Calculating the approximate volume, we get $V \approx 3419.5328$ cubic feet.
Round to Nearest Tenth: Calculating the approximate volume, we get $V \approx 3419.5328$ cubic feet.Rounding to the nearest tenths place, the volume of the cylinder is approximately $3419.5$ cubic feet.

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