Question

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 aluminum sheet. The diameter of the model is $3$cm and its length is $12$cm. If each cone has a height of $2$cm, then 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

Here, radius of cylindrical portion $=\frac{3}{2}$cm

Height of each cone$=2$cm

Height of cylindrical portion$=12-2-2=8$cm

Volume of the air contained in the model $=$Volume of the cylindrical portion of the model $+$ Volume of two conical ends.

$=\pi r^2{h}_1+2\times \frac{1}{3}\pi r^2{h}_2=\pi r^2(h_1+\frac{2}{3}{h}_2)$

$=\pi \times {\left(\frac{3}{2}\right)}^2\times (8+\frac{2}{3}\times 2)$

$=\frac{22}{7}\times \frac{9}{4}\times \frac{28}{3}=66{cm}^3$