Home » Maths for Planet Earth » Storing Sequestrates

Storing Sequestrates

Facebook
Twitter
Pinterest
Print

A manufacturer produces a tank for storing liquid CO2 underground.

The tank is modelled in the shape of a hollow vertical circular cylinder closed with a flat lid at the top and a hemispherical shell at the bottom. 

The walls of the tank are assumed to have negligible thickness.

The cylinder has a radius r metres and height h metres and the hemisphere has radius r metres.

The volume of the tank is 6 m3.

a) Show that, according to the model, the surface area of the tank, in m2 is given by

\[\frac{12}{r} + \frac{5}{3}\pi r^{2}\]

[4 marks]

The manufacturer needs to minimise the surface area of the tank, to minimise costs. 

b) Find, using calculus, the radius of the tank for which the surface area is a minimum.

[4 marks]

c) Find the surface area of the tank for this radius, giving your answer to the nearest integer.

[2 marks]

Start exploring

Latest from blog

More Maths for Planet Earth

A Level
15 cities, each of varying sizes, decide to have carbon-neutral public transport systems. When the cities are arranged in size order from smallest to
A Level
2 deep sea ocean currents meet. By modelling one current as the positive y axis. a) Find the angle that the second current, with
A Level
A country wishes to achieve net-zero CO2 emissions in 50 years.  At the start of the program their emissions are 800MtCO2 year-1.  They decide
A Level
A hurricane is heading from the Atlantic Ocean to Miami, Florida. If the centre of the hurricane goes within a 50 kilometre radius of