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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? ◻

A miniature basketball in the shape of a sphere has a volume of approximately 113113 cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?\newline◻

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Q. A miniature basketball in the shape of a sphere has a volume of approximately 113113 cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?\newline◻
  1. Volume Formula: We know the volume of a sphere is given by the formula V=43πr3 V = \frac{4}{3}\pi r^3 , where V V is the volume and r r is the radius of the sphere. We are given the volume V=113 V = 113 cubic inches. We need to solve for r r .
  2. Rearranging Formula: First, let's rearrange the formula to solve for r r . We get r3=3V4π r^3 = \frac{3V}{4\pi} .
  3. Substitute Values: Now, we plug in the given volume and the approximate value of π \pi into the rearranged formula. Using π≈3.14 \pi \approx 3.14 , we have r3=3×1134×3.14 r^3 = \frac{3 \times 113}{4 \times 3.14} .
  4. Calculate Value: Let's calculate the value inside the cube root: r3=33912.56 r^3 = \frac{339}{12.56} .
  5. Cube Root: Performing the division, we find r3≈26.9936 r^3 \approx 26.9936 .
  6. Final Radius Calculation: To find the radius r r , we take the cube root of r3 r^3 . So, r≈26.99363 r \approx \sqrt[3]{26.9936} .
  7. Final Radius Calculation: To find the radius r r , we take the cube root of r3 r^3 . So, r≈26.99363 r \approx \sqrt[3]{26.9936} .Using a calculator, we find that r≈3.00 r \approx 3.00 inches when rounded to the nearest inch.

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