# Thread: diameter of cylinder

1. ## diameter of cylinder

A Pluming Firm is required to make a copper cylinder of 155 letres capacity, to fit into a smaller then usual airing cupboard in which the maximum diamiter of the cylinder must not exced 425mm. How high will the cylinder need to be? need to know working out, so i can understand it.

2. Originally Posted by ASSC
A Pluming Firm is required to make a copper cylinder of 155 letres capacity, to fit into a smaller then usual airing cupboard in which the maximum diamiter of the cylinder must not exced 425mm. How high will the cylinder need to be? need to know working out, so i can understand it.
You and someone else here are apparently in the same class. I'll tell you what I told them. The volume of a cylinder is
V = (pi)r^2*h = (pi)(d/2)^2*h = (pi/4)d^2*h

You know V, and you know the maximum diameter. So you can find h.

-Dan

3. Originally Posted by ASSC
A Pluming Firm is required to make a copper cylinder of 155 letres capacity, to fit into a smaller then usual airing cupboard in which the maximum diamiter of the cylinder must not exced 425mm. How high will the cylinder need to be? need to know working out, so i can understand it.
Hi,

the first step should be to convert all measures into one common unit:

155 litres = 155 dm³ = 155000 cm³
425 mm = 42.5 cm

The volume of a cylindre is
V = pi*r^2*h
You know the volume and you know the maximum radius (= half of the maximum diameter). Therefore you've got the equation:

155000 cm³ = pi * (21.25 cm)² * h

Solve for h:

h = (155000 cm³)/(pi * 451.5625 cm²) ≈ 109.3 cm

In this calculation the thickness of the material was not taken into consideration.

EB