(a)

The function is  and the interval is .

(i)

The surface area formula, for rotation about the - axis is .

Consider .

Differentiate the function with respect to .

Substitute corresponding values in .

The surface area :

The surface area of the curve obtained after rotation about - axis is .

(ii)

The surface area formula, for rotation about the - axis is .

Substitute corresponding values in .

The surface area :

The surface area of the curve obtained after rotation about - axis is .

(b)

From part (a) :

(i)

The surface area of the curve obtained after rotation about - axis is .

Using a calculator, the value of is .

From part (a) :

(ii)

The surface area of the curve obtained after rotation about - axis is .

Using a calculator, the value of is .

(a)

(i) .

(ii) .

(b)

(i) .

(ii) .