Home » Maths for Planet Earth » Storing Sequestrates

Storing Sequestrates


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
Human-induced global warming is causing deserts such as the Sahara to increase in surface area. In 1950 the area of the Sahara Desert was
The table shows information about sea level rise due to human-induced climate change. (mm = millimetres). Sea level rise in 2006 (mm) Sea level
A Level
2 weather-monitoring satellites orbit the earth. One is in a circular orbit C₁, the other orbits in an extreme ellipse, C₂ so that it can
Here is a pie chart taken from Mike Berners-Lee’s book There is no Planet B.  a) Calculate angle x. (shown on graph in the