The area of the surface generated by revolving the curve x = 3 cos t, y = 3 sin t, 0 $\le$ t $\le$ $\pi$ about the x-axis is
A) 9 $\pi$
B) 36
C) 18 $\pi$
D) 45 $\pi$
E) 36 $\pi$

Question

The area of the surface generated by revolving the curve x = 3 cos t, y = 3 sin t, 0 $\le$  t $\le$ $\pi$ about the x-axis is
A) 9 $\pi$
B) 36
C) 18 $\pi$
D) 45 $\pi$
E) 36 $\pi$

Quizplus · Accepted Answer

The curve described by $x = 3\cos(t)$ and $y = 3\sin(t)$ for $0 \leq t \leq \pi$ represents a semicircle of radius 3. When this semicircle is revolved around the x-axis, it generates a sphere of radius 3. The surface area of a sphere is given by $4\pi r^2$. Substituting $r = 3$ gives $4\pi(3)^2 = 36\pi$, which corresponds to choice E.

The Area of the Surface Generated by Revolving the Curve ≤\le≤

The Area of the Surface Generated by Revolving the Curve $\le$