Question

the radius and height of a cylinder increased by 20% find the percentage increase in its volume​

Answer 1

Answer:

72.8%

Step-by-step explanation:

Let the initial radius be 'r' and initial height be 'h'.

Therefore, initial volume= (π)(r)^2(h)

Now, since there is 20% increase in height and radius,

therefore the new radius,

=(r)+20%(r)

=(r)+1/5(r)

=6/5(r)

And new height,

=(h)+20%(h)

=(h)+1/5(h)

=6/5(h)

Therefore now the new volume,

=(π)(6/5(r))^2(6/5(h))

=(π)(36/25(r)^2)(6/5(h))

Now the difference in two volumes,

=[(π)(36/25(r)^2)(6/5(h))]-[(π)(r)^2(h)]

=[(π)(r)^2(h)][(36/25)×(6/5)-1]

=[(π)(r)^2(h)][1.728-1]

=[(π)(r)^2(h)][0.728]

Therefore the percentage increase in volume,

=(difference in volume)÷(initial volume)×100%

={[(π)(r)^2(h)][0.728]}÷[(π)(r)^2(h)]×100%

=0.728×100%

=72.8%

.

-ISHAN