Question

the volume of a sphere with radius r is given by the formula $v=\frac{4}{3}pi r^{3}$. find the volume of a sports ball with radius 6 cm is cm.³ use 3.14 or the π key on your calculator. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Substitute radius value

Substitute $r = 6$ into $V=\frac{4}{3}\pi r^{3}$, we get $V=\frac{4}{3}\pi\times6^{3}$.

Step2: Calculate $6^{3}$

$6^{3}=6\times6\times6 = 216$, so $V=\frac{4}{3}\pi\times216$.

Step3: Simplify the expression

$\frac{4}{3}\times216 = 4\times72=288$, then $V = 288\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14$, we have $V\approx288\times3.14 = 904.32$.

Step5: Round the answer

Rounding $904.32$ to the nearest tenth gives $904.3$.

Answer:

$904.3$