Question

2.3
score: 16.67/19 answered: 17/19
question 18
the volume of a sphere is given by
v(r)=\frac{4}{3}pi r^{3}
where (r) is the radius. find the volume, in cubic inches, when the radius is 6 inches.
either enter an exact answer in terms of (pi) or round off to 3 decimal places.
cubic inches
question help: ebook written example

Explanation:

Step1: Substitute radius value

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

Step2: Calculate $6^{3}$

$6^{3}=6\times6\times6 = 216$. Then $V(6)=\frac{4}{3}\pi\times216$.

Step3: Multiply fractions

$\frac{4}{3}\times216 = 4\times72=288$. So $V(6)=288\pi$.
If we want a decimal - approximation, using $\pi\approx3.14159$, then $V(6)\approx288\times3.14159 = 904.779$.

Answer:

$288\pi$ (exact) or $904.779$ (approximate)