Question

consider a sphere with a diameter of 19.8 cm. using the aleks calculator, approximate the volume of the sphere. to do the approximation, do not round any intermediate steps, and use the π button on the calculator. round your answer to the nearest hundredth. if necessary, refer to the list of geometry formulas. make sure that you use the correct units in your answer. approximate volume: 4069 cm³

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter. Given diameter $d = 19.8$ cm, so $r=\frac{d}{2}=\frac{19.8}{2}=9.9$ cm.

Step2: Use the volume formula

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 9.9$ cm into the formula: $V=\frac{4}{3}\pi(9.9)^{3}$.

Step3: Calculate the volume

$V=\frac{4}{3}\pi\times970.299$. Using the $\pi$ - button on the calculator, $V=\frac{4\times970.299\pi}{3}\approx\frac{4\times970.299\times3.14159}{3}$.
$V\approx4069.43$ cm$^{3}$. Rounding to the nearest hundredth, $V\approx4069.43$ cm$^{3}$.

Answer:

$4069.43$ cm$^{3}$