If the total surface area of a right circular cylinder is $168 \pi$ square meters and a radius of the base is 6 meters long, find the height of the cylinder.
A) $6 \pi$ meters
B) $16$ meters
C) $8$ meters
D) $24$ meters
E) none of these

Question

Quizplus · Accepted Answer

Let $h$ be the height of the cylinder. The lateral area of the cylinder is $2\pi rh$, which is equal to $(168-2\pi(6^2)) 	ext{m}^2$. Simplifying, we find $2\pi rh = 72\pi$. Dividing both sides by $2\pi r$ gives $h=\frac{36}{r}$. Substituting $r=6$, we get $h=\boxed{6 	ext{ m}}$.

If the Total Surface Area of a Right Circular Cylinder 168π168 \pi168π

If the Total Surface Area of a Right Circular Cylinder $168 \pi$