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:

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 for a sphere

The volume formula of 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

Using a calculator with the $\pi$ - button:
$V=\frac{4}{3}\pi\times(9.9)^{3}=\frac{4}{3}\pi\times970.299\approx\frac{4\times3.14159\times970.299}{3}\approx4069.4$ $cm^{3}$

Answer:

$4069$ $cm^{3}$