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 mathrm{~cm} )
b) about ( 12.8 mathrm{~cm} )
c) about ( 1.9 mathrm{~cm} )
d) about ( 4.9 mathrm{~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. \(r=\sqrt[3]{119.43}\approx4.9\)

Answer:

D. About \(4.9\) cm