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Specialist2025 NHT Exam 1 · Q8Tech-free4 marks

Surface area of revolution of a parametric curve

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Consider the curve shown below.

The parametric equations for this curve are

$x = 4\cos^3(\theta) \text{ and } y = 4\sin^3(\theta), \text{ where } \theta \in \left[0, \frac{\pi}{2}\right].$

Find the area of this surface.

4 marks

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3

(

θ

)

,

where

θ

∈

[0,2π].

The curve is rotated about the $y$ -axis to form a surface of revolution.

Axes with x from −4 to 4 and y from −1 to 4, showing a concave-up curve in the first quadrant running from (0, 4) on the y-axis down to (4, 0) on the x-axis.