Question

radius the radius r in inches of a sphere can be approximated by $r = \sqrt3{\frac{21v}{88}}$, where v is the volume of the sphere in cubic inches. find the approximate radius of a sphere that has a volume of 38,808 cubic inches.

inches

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Explanation:

Step1: Substitute V with 38808

We know the formula for the radius \( r = \sqrt[3]{\frac{21V}{88}} \), and \( V = 38808 \). So we substitute \( V \) into the formula: \( r=\sqrt[3]{\frac{21\times38808}{88}} \)

Step2: Calculate the numerator

First, calculate \( 21\times38808 \). \( 21\times38808 = 814968 \)

Step3: Calculate the fraction

Then, divide the result by 88: \( \frac{814968}{88}=9261 \)

Step4: Take the cube root

Now, we need to find the cube root of 9261. Since \( 21\times21\times21 = 9261 \), so \( \sqrt[3]{9261}=21 \)

Answer:

21