SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Volume, SM-Bank 014

A closed cylindrical water tank has external diameter 3.5 metres.

The external height of the tank is 2.4 metres.

The walls, floor and top of the tank are made of concrete 0.25 m thick.
 

Geometry and Trig, FUR2 2006 VCAA 3

  1. What is the internal radius, \(r\), of the tank?  (1 mark)

  2. What is the internal height, \(h\), of the tank?  (1 mark)

  3. Determine the maximum amount of water this tank can hold.
    Write your answer correct to the nearest cubic metre.  (2 marks) 

Show Answers Only

a.    \(1.5\ \text{m}\)

b.    \(13\ \text{m}^3\ \text{(nearest m³)}\)

Show Worked Solution

a.   \(\text{Internal radius}\ (r)\)

\(=\dfrac{1}{2}\times (3.5-2\times 0.25)\)

\(=1.5\ \text{m}\)
 

b.    \(\text{Internal Height}\ (h)\) \(=2.4-(2\times 0.25)\)
    \(=1.9\ \text{m}\)

 

c.    \(\text{Volume}\) \(=\pi r^2 h\)
    \(=\pi\times 1.5^2\times 1.9\)
    \(=13.430\dots\)
    \(=13\ \text{m}^3\ \text{(nearest m³)}\)