Question

Height of a hollow right circular cylinder, open at both ends, is 2.8 metre. If length of inner
diametre of the cylinder is 4.6 dem and the cylinder is made up of 84.48 cubic dcm of iron,
let us calculate the length of outer diameter of the cylinder.​

Answer 1

Given,

The height of the cylinder is = 2.8 metres = 28 dcm

The inner diameter of the cylinder = 4.6 dcm

The volume of the cylinder = 84.48 dcm³

To find,

The outer diameter of the cylinder.

Solution,

Let,the outer  radius of the cylinder = x dcm

[Assume,x as a variable to do the further mathematical calculations.]

The volume of the whole cylinder including the hollow space = π×x²×28 = 22/7 × x² × 28 = 88x² dcm³

The volume of the cylinder excluding the hollow space = π × (4.6)² × 28 = 22/7 × 21.16 × 28 = 1862.08 dcm³

Now,the volume of iron = volume including hollow space - volume excluding hollow space = 1862.08-88x² dcm³

Now,if you compare the volume of iron that we have calculated and the volume of iron that is given in the question then we will get the following mathematical equation,

1862.08-88x² = 84.84

-88x² = 84.84-1862.08

-88x² = -1777.24

88x² = 1777.24

x² = 20.19

x = 4.49

x = 4.5 (approx.)

Outer diameter = 4.5×2 = 9 dcm

Hence,the approximate value of the outer diameter is 9 dcm.