Solve the problem.
-The equation $r = \sqrt [ 3 ] { \frac { 3 V } { 4 \pi } }$ gives the radius $r$ of a sphere of volume $V$. If the radius of a sphere is 6 in., find the exact volume.
A) $96 \pi \mathrm { in. } ^ { 3 }$
B) $288 \pi \mathrm { in } ^ { 3 }$
C) $144 \pi$ in. $^ { 3 }$
D) $\sqrt [ 3 ] { \frac { 9 } { 2 \pi } }$ in. ${ } ^ { 3 }$

Question

Quizplus · Accepted Answer

Given the formula $r = \sqrt [ 3 ] { \frac { 3 V } { 4 \pi } }$ and $r = 6$ in., we substitute $r$ into the equation and solve for $V$: $6 = \sqrt [ 3 ] { \frac { 3 V } { 4 \pi } }$. Cubing both sides gives $216 = \frac { 3 V } { 4 \pi }$, and solving for $V$ gives $V = 288 \pi$ in.$^3$.

Solve the Problem r=3V4π3r = \sqrt [ 3 ] { \frac { 3 V } { 4 \pi } }r=34π3V​​

Solve the Problem $r = \sqrt [ 3 ] { \frac { 3 V } { 4 \pi } }$