3.24: Related rates in a triangular prism water container

0606/21/M/J/22 — Question 9 · 8 marks

All lengths are in metres. A water container is a triangular prism of length

5

. The water forms a prism with equilateral triangular cross-section of side

x

and depth

h

(a)

Show that the volume

V

of the water is given by

V = \dfrac{5\sqrt{3}}{3}h^{2}

[4]

(b)

Water is pumped in at

0.5\,\mathrm{m}^{3}

per minute. Find the rate at which the depth is increasing when the depth is

0.1\,\mathrm{m}

[4]