A miniature basketball in the shape of a sphere has a volume of approximately 113 cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

Question

Bytelearn · Accepted Answer

Given Volume and Formula: We know the volume of a sphere is given by the formula $ V = \frac{4}{3}\pi r^3 $, where $ V $ is the volume and $ r $ is the radius of the sphere. We are given the volume $ V = 113 $ cubic inches.Rearranging Formula: To find the radius, we need to rearrange the formula to solve for $ r $. The rearranged formula is $ r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}} $.Calculating Radius: We know $ V = 113 $ cubic inches and $ \pi \approx 3.14 $. Let's plug these values into the rearranged formula to calculate the radius. $ r = \left(\frac{3 \times 113}{4 \times 3.14}\right)^{\frac{1}{3}} $Calculate Numerator: First, calculate the numerator $ 3 \times 113 = 339 $.Calculate Denominator: Next, calculate the denominator $ 4 \times 3.14 = 12.56 $.Divide Numerator by Denominator: Now, divide the numerator by the denominator $ \frac{339}{12.56} \approx 26.9936 $.Find Cube Root: Finally, take the cube root of the result to find the radius $ r \approx \left(26.9936\right)^{\frac{1}{3}} $.Cube Root Calculation: Using a calculator, the cube root of $ 26.9936 $ is approximately $ 3.00 $ inches.Round to Nearest Inch: Round the radius to the nearest inch, which gives us $ 3 $ inches.

A miniature basketball in the shape of a sphere has a volume of approximately $113$ cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

Full solution

More problems from Pythagorean Theorem and its converse

Related topics

A miniature basketball in the shape of a sphere has a volume of approximately 113113113 cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

A miniature basketball in the shape of a sphere has a volume of approximately $113$ cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?