Question

The formula for the volume of a sphere is V = 4/3πr^³, where V is the volume and r is the radius. Solve the formula for r, and then use it to answer the question. The volume of a basketball is about 435 cubic inches. What is the radius of the basketball, to the nearest tenth of an inch? Use 3.14 for π.

a) 4.5 inches
b) 4.7 inches
c) 4.1 inches
d) 4.3 inches

Answer 1

To find the radius of a basketball given its volume of 435 cubic inches, the volume formula for a sphere was rearranged. Using 3.14 for pi, the radius was calculated to be approximately 4.7 inches, which is option b).

Step-by-step explanation:

The formula given for the volume of a sphere is V = 4/3πr^3. To solve for the radius (r), we must rearrange this formula, which involves solving the equation for r when given the volume (V). In this instance, the volume of a basketball is said to be about 435 cubic inches. We will be using 3.14 for π (pi).

First, we rearrange the formula to solve for r:

1. Multiply both sides by 3/4 to get rid of the fraction on the right: V(3/4) = πr^3
2. Divide both sides by π to isolate r^3: (3V)/(4π) = r^3
3. Take the cube root of both sides to solve for r: r = ∛((3V)/(4π))

Plugging the given volume V = 435 cubic inches into the rearranged formula, we have:

r = ∛((3×435)/(4×3.14)) ≈ ∛((1305)/(12.56)) ≈ ∛103.82 ≈ 4.7 inches

Therefore, the radius of the basketball, to the nearest tenth of an inch, is approximately 4.7 inches, which corresponds to option b).