A large industrial hopper in the shape of an inverted square-based pyramid is being filled with fine grain at a constant rate of $cm3/s24\text{ cm}^3/\text{s}$ .

After $t$ seconds, the depth of the grain in the hopper is $cmh\text{ cm}$ . The apex of the pyramid is at the bottom.

When the depth of the grain is $cmh\text{ cm}$ , the volume $cm3V\text{ cm}^3$ of the grain is given by

\frac{2}{9}h^3

Show that when $t = 3$ ,

\frac{dV}{dh} = 12\sqrt[3]{18}

Hence, find the rate at which the depth of the grain is increasing when $t = 3$ . Give your answer to three significant figures.

A large industrial hopper in the shape of an inverted square-based pyramid is being filled with fine grain at a constant rate of $cm3/s24\text{ cm}^3/\text{s}$ .

After $t$ seconds, the depth of the grain in the hopper is $cmh\text{ cm}$ . The apex of the pyramid is at the bottom.

When the depth of the grain is $cmh\text{ cm}$ , the volume $cm3V\text{ cm}^3$ of the grain is given by

\frac{2}{9}h^3

Show that when $t = 3$ ,

\frac{dV}{dh} = 12\sqrt[3]{18}

Hence, find the rate at which the depth of the grain is increasing when $t = 3$ . Give your answer to three significant figures.

3.6.5 Differentiation (A-level only)

Question 92

Markscheme

3.6.5 Differentiation (A-level only)

Question 92

Markscheme

3.6.5 Differentiation (A-level only)

Question 92

3.6.5 Differentiation (A-level only) Questions

3.6.5 Differentiation (A-level only)

Question 92

3.6.5 Differentiation (A-level only) Questions