Question

the formula for the volume of a sphere is $v = \frac{4}{3}\pi r^3$, 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 $\pi$. \\(\bigcirc\\) a. 4.7 inches \\(\bigcirc\\) b. 4.5 inches \\(\bigcirc\\) c. 4.3 inches \\(\bigcirc\\) d. 4.1 inches

Explanation:

Step1: Isolate $r^3$ in formula

Start with $V=\frac{4}{3}\pi r^3$. Rearrange to solve for $r^3$:
$$r^3=\frac{3V}{4\pi}$$

Step2: Substitute given values

Plug in $V=435$, $\pi=3.14$:
$$r^3=\frac{3\times435}{4\times3.14}=\frac{1305}{12.56}\approx103.90$$

Step3: Calculate cube root of result

Find $r$ by taking the cube root:
$$r=\sqrt[3]{103.90}\approx4.1$$

Answer:

D. 4.1 inches