A cylindrical can has radius and height

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A cylindrical can has radius

r

and height

h

, both changing with time. At an instant when

r = 3\text{ cm}

and

h = 10\text{ cm}

, the radius increases at

0.10\text{ cm/s}

and the height increases at

0.20\text{ cm/s}

. What is the instantaneous rate of change of the can’s volume? (a)

6\pi\text{ cm}^{3}\!\big/\!\text{s}

(b)

12.9\pi\text{ cm}^{3}\!\big/\!\text{s}

(c)

7.8\pi\text{ cm}^{3}\!\big/\!\text{s}

(d)

1.8\pi\text{ cm}^{3}\!\big/\!\text{s}