Question

if a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each, then by how much per cent does the volume of the solid increase?​

Answer 1

The volume of the cylinder gets changed by 2 whole of 1/100%.

Step-by-step explanation:

Let, the radius of the cylinder be, 'r'

The height of the cylinder be, 'h'

∴ Volume of the cylinder = πr²h

After heating, the radius of the cylinder becomes,

r+ (r*1/100)

= r+r/100

=(100r+r)/100 [∵ The L.C.M. of the denominators is 100.]

= 101r/100

∴ New volume of the cylinder

= π(101r/100)²h

= 10201πr²h/10000

∴ The change in volume_

(10201πr²h/10000) - πr²h

=(10201πr²h - 10000πr²h)/10000 [∵ The L.C.M. of the dinominators is 10000]

= 201πr²h/10000

∴ The changed % in volume_

{(201πr²h/10000)/πr²h}*100

= (201πr²h*100)/ (10000*πr²h)

= 201/100

= 2 whole of 1/100 %.