If a cylinder has a surface area of 25 square metres and a diameter of 100 cm, what is its height in metres?

To determine the height of a cylinder when given the surface area and diameter, it is essential to use the formula for the surface area of a cylinder. The total surface area ( A ) of a cylinder is given by the formula:

[

A = 2\pi r(h + r)

]

where:

• ( r ) is the radius of the cylinder,

• ( h ) is the height of the cylinder,

• ( \pi ) is approximately 3.14159.

In this case, the diameter of the cylinder is given as 100 cm, which means the radius ( r ) is half of the diameter:

[

r = \frac{diameter}{2} = \frac{100, \text{cm}}{2} = 50, \text{cm} = 0.5, \text{m}

]

We now know that the surface area ( A ) is 25 square metres. Plugging the values into the surface area formula gives us:

[

25 = 2\pi(0.5)(h + 0.5)

]

Simplifying this equation leads to the following steps:

1. Substitute ( r ) into the