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

Answer:

Let initial radius and height of cylinder be 'r' and 'h' respectively

Initial volume, V

1

=πr

2

h

New radius=r+1 % of r=1.01r

New height=h+1% of 1.01h

New volume,V

2

=π(1.01r)

2

×1.01h=1.0303πr

2

h

% increase in volume=

πr

2

h

(1.0303−1)πr

2

h

×100=3.03%

Answer 2

Solution ♡

Let initial radius and height of cylinder be 'r' and 'h' respectively

Initial volume, V₁

➞ πr²h

New radius = r+1 % of r = 1.01r

New height = h+1% of 1.01h

New volume,V₂

➞ π(1.01r)² × 1.01h

➞ 1.0303πr² h

% increase in volume

πr²h(1.0303 - 1) πr²h / πr²h + 100

➞ 3.03 %