Question

question 9 (mandatory) (1 point) saved the equation $v = \frac{4}{3}\pi r^{3}$ gives the volume, v, of a sphere with radius r. determine the radius of a sphere with volume $500 \mathrm{cm}^{3}$. a) about 2.3 cm b) about 12.8 cm c) about 1.9 cm d) about 4.9 cm

Explanation:

Step1: Substitute \( V = 500\) into the formula

Given \( V=\frac{4}{3}\pi r^{3}\), substitute \( V = 500\). So, \(500=\frac{4}{3}\pi r^{3}\).

Step2: Solve for \( r^{3}\)

First, multiply both sides by \(\frac{3}{4}\) to get \(r^{3}=\frac{3\times500}{4\pi}\).

$$r^{3}=\frac{1500}{4\pi}=\frac{375}{\pi}\approx\frac{375}{3.14}\approx119.43$$

Step3: Solve for \( r\)

Take the cube - root of both sides. \(r=\sqrt[3]{119.43}\approx4.9\) (using a calculator for \(\sqrt[3]{119.43}\))

Answer:

d) About \(4.9\) cm