Question

Three cylinders each of height 8 cm and radius 2 cm are placed on a plane so that each touches the other two. Find the volume of the region bounded by 3 cylinders.

Answer 1

Here is a similar question with its sol


Q)Three cylinders each of height 16 cm
and radius of base 4 cm are placed on
a plane so that each cylinder touches
. the other two cylinders.
Then the volume of the region
enclosed between the three cylinders

Solution:-

Draw the cross section of the region. The cylinders will be represented by circles.
Join the centers of the circles to form an equilateral triangle with a side of length 2r = 8cm

Area of an equilateral triangle = (√3/4)a²
a = 8
Area = 16√3 cm²

There are three equal sectors included in this area, each with an angle of 60°
Area of the three sectors = 3×(60/360)×π×4²
Area of the sectors = 8π cm²

Area between the circles = (16√3 - 8π)cm²
= 8(2√3 - π)cm²

Volume between the cylinders = Area × height
= 8(2√3 - π)cm² × 16
= 128(2√3 - π)cm²