1

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 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.)

Open in App

Solution

The correct option is **B**

66 cm3

Diameter of Cylinder = Diameter of Cones = 3 cm

⇒ Radius of Cylinder = Radius of Cones =r=32=1.5 cm

Height of each cone =h1=2 cm

Length of model = 12 cm

Height of Cylinder, h

= Total Height of Model - height of 1st Cone - height of 2nd Cone

=12−2−2=8 cm

Volume of air in the model

= Volume of Solid

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

We know that, volume of a cylinder of radius r and height h is πr2h and volume of a cone of radius R and height H is given by 13πR2H.

Therefore, volume of air in the model

=πr2h+13πr2h1+13πr2h1

=πr2(h+h13+h13)

=227×1.5×1.5(8+43)

=227×1.5×1.5(283)=66 cm3

0

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program