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 aluminium sheet.The diameter of the model is 3cm and its length is 12cm.If each cone has a height of 2cm,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.) merit nation experts please send me the video so that i can understand properly.

Answer 1

volume of the container=2/3πr²h+πr²h,
so the height of the cylinder=8cm.
and thus the volume=66cm³.

Answer 2

Volume of Air Contained in Model

= Volume of Model

= Volume of Cylinder + Volume of 1st cone + Volume of 2nd Cone

= πr²h + 1/3πr²h + 1/3πr²h

= (π × r² × h) + (1/3 × π × r² × h) + (1/3 × π × r² × h)

= (22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h)

= (22/7 × 9/4 × h) + (1/3 × 22/7 × 9/4 × 2) + (1/3 × 22/7 × 9/4 × h)

= (198/28 × h) + (22/217 × 9/4 × h) + (22/21 × 9/4 × h)

= (198/28 × (12 - 4)) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)

= (198/28 × 8) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)

= (198/28 × 8) + (22/21 × 9/2 × 1) + (22/21 × 9/2 × 1)

= (198/28 × 8) + (22/21 × 9/2) +  (22/21 × 9/2)

= (1584/28) + (198/42) + (198/42)

= (56.57) + (4.71)  + (4.71)

= 65.99 cm³

≈ 66 cm³