Question

the volume of a sphere is 998 cm³. what is the approximate radius of the sphere? use the formula v = \frac{4}{3}\pi r³ and 3.14 for \pi. a. 4.3 cm b. 6.2 cm c. 7.5 cm d. 13.3 cm e. 15.4 cm

Explanation:

Step1: Substitute values into formula

Given $V = 998$ and $\pi=3.14$, we have $998=\frac{4}{3}\times3.14\times r^{3}$.

Step2: Solve for $r^{3}$

First, simplify the right - hand side: $\frac{4}{3}\times3.14\times r^{3}=\frac{12.56}{3}r^{3}$. Then, $r^{3}=\frac{998\times3}{12.56}$. Calculate $998\times3 = 2994$, so $r^{3}=\frac{2994}{12.56}\approx238.376$.

Step3: Solve for $r$

Take the cube - root of both sides: $r=\sqrt[3]{238.376}$. Using a calculator, $r\approx6.2$ cm.

Answer:

B. 6.2 cm