Question

A family is replacing the cylindrical hot
water boiler of the house. They cannot
change the height of the boiler but they
can double its diameter. If the previous
tank could hold 100 litres, can we predict
what the new tank will hold? What would
happen if the diameter of the tank is tripled?

Answer 1

If the tank doubles its diameter the volume will be 400 liters and if its diameter triples the volume will be 900 liters

Explicación paso a paso:

The volume of a cylindrical body is

V = πr²h

• Volume new tank with double diameter

V = π (2r) ²h = 4πr²h

If the height value is constant, the resulting ratio indicates that the volume will increase 4 times its value, that is:

V = 4 * 100L

Vf = 400 liters

• If the tank triples its diameter value

V = π (3r) ²h = 9πr²h

The volume increases nine times its previous value

Vf = 900 liters