Shubham pal an engineering student was asket to make a model shaped like cylinder wih 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 32 cm , find the volufme of air contained i the model that shubham pal made. (Assume the outer and inner dimensions of the model to be nearly the same).

Explanation

Given model is a combination of a cylinder and two cones .Also have diameter of the model BC=ED=3cm
`r=(3)/(2)`=1.5 cm
Height of cone `h_(1)`=2cm and length of the model ,AF=12 cm

Height of cylinder `h_(2)`=8cm
Now volume of the air inside the model
=volume of air inside (cone+cylinder+cone)
`=((1)/(3)pir^(2)h_(1)+pir^(2)h_(2)+(21)/(3)pi(1)/(3)pir^(2)h_(1))=(1)/(3)pir^(2)(h_(1)+3h_(2)+h_(1))`
`=(1)/(3)xx(22)/(7)xx1.5xx1.5(2+3xx8+2)=(22)/(7)xx(2.25)/(3)xx(2+24+2)`
`=(22)/(78)xx0.75xx28=22xx3=66 cm^(3)`