Question

Find the area of the surface obtained by revolving the given curve about the indicated axis.?

y = 9 − x^2 on [0, 3]; y−axis

Answer 1

Step 1 :

The function is and the interval is .

For rotation about the y - axis, the surface area formula : .

The function is .

Solve for x .

The function is .

Differentiate the curve with respect to y .

Evaluating boundaries :

If , then .

If , then .

Step 2 :

Substitute corresponding values in .

The surface area is .

Let , then .

Evaluating boundaries :

If , then .

If , then .

Substitute corresponding values in .

The area of the surface by rotating the curve about the y - axis is 117.32 square units.

Solution :

The area of the surface by rotating the curve about the y - axis is 117.32 square units.