Question

a cone has a volume of 640.56 cubic feet and a height of 17 feet. what is its radius? round your answer to the nearest hundredth.
r ≈ \boxed{} feet
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Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 640.56 \) cubic feet and \( h=17 \) feet. We need to solve for \( r \).

Step2: Substitute the known values into the formula

Substitute \( V = 640.56 \) and \( h = 17 \) into the formula:

$$ 640.56=\frac{1}{3}\pi r^{2}(17) $$

Step3: Solve for \( r^{2} \)

First, multiply both sides by 3 to get rid of the fraction:

$$ 640.56\times3=17\pi r^{2} $$

$$ 1921.68 = 17\pi r^{2} $$

Then, divide both sides by \( 17\pi \):

$$ r^{2}=\frac{1921.68}{17\pi} $$

We know that \( \pi\approx3.14 \), so:

$$ r^{2}=\frac{1921.68}{17\times3.14} $$

Calculate the denominator: \( 17\times3.14 = 53.38 \)
Then, \( r^{2}=\frac{1921.68}{53.38}\approx36 \)

Step4: Solve for \( r \)

Take the square root of both sides:

$$ r=\sqrt{36}= 6 $$

(We take the positive square root since radius cannot be negative)

Answer:

\( r\approx\boxed{6.00} \) (rounded to the nearest hundredth)