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.

1.6 Differentiation

Question 53

Markscheme

1.6 Differentiation

Question 53

Markscheme

1.6 Differentiation

Question 53

1.6 Differentiation Questions

1.6 Differentiation

Question 53

1.6 Differentiation Questions