Question

Question 2
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Answer 1

Height of cylinder $=12–4=8$ cm, radius $=1.5$ cm, height of cone $=2$ cm
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times {1.5}^2\times 8$
$=18\pi c{m}^3$
Volume of a cone
$=\frac{1}{3}\pi \times {1.5}^2\times 2$
$=1.5\pi c{m}^3$
Total volume= Volume of cylinder +2 Volume of a cone
$=1.5\pi +1.5\pi +18\pi$
$=21\pi =66c{m}^3$