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Chapter 6: Q 65 (page 525)

Prove that a shell with average radius r, height h, and thickness role="math" localid="1651773320324" 鈭�xhas volumeV=2蟺谤丑鈭�x.

Short Answer

Expert verified

By dividing the shell into different cuboids, we get that the volume of a shell is :-

V=2蟺谤丑鈭�x

Step by step solution

01

Step 1. Given Information

We have to prove that volume of a shell with radius r, height hand thickness鈭�xisV=2蟺谤丑鈭�x.

02

Step 2. Volume of a shell

We have a shell with

radius=r,height=handthickness=鈭�x

if we divide the shell into several equal cuboids, then we know that the volume of a cuboid is defined as length脳breadth脳height.

So the volume of cuboid will be role="math" rh鈭�x.

if we make a complete circle of cuboids, then we get the shell. So the volume of shell will be equals to the 2蟺times the volume of a cuboid as 2蟺is represents a circle.

So the volume of shell is :-

V=2蟺脳volumeofcuboid鈬�V=2蟺谤丑鈭�x

Hence proved.

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