Question

1. if the volume of a sphere is 523.6 cubic meters, which of the following could be its radius?

a. 7 meters
b. 5 meters
c. 3 meters
d. 10 meters

Explanation:

Step1: Recall sphere volume formula

The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$, where $V$ is volume and $r$ is radius.

Step2: Rearrange to solve for $r$

Rearrange the formula to isolate $r$:
$$r = \sqrt[3]{\frac{3V}{4\pi}}$$

Step3: Substitute $V=523.6$

Substitute the given volume into the formula:
$$r = \sqrt[3]{\frac{3\times523.6}{4\times3.14}}$$

Step4: Calculate the inner expression

First compute the numerator and denominator:
$\frac{3\times523.6}{4\times3.14} = \frac{1570.8}{12.56} = 125$

Step5: Compute the cube root

Find the cube root of 125:
$r = \sqrt[3]{125} = 5$

Answer:

b. 5 meters