If a cylinder has a surface area of 15 square metres and a diameter of 95 cm, what is its height in metres?

To determine the height of a cylinder when given its surface area and diameter, one must understand the relationship between a cylinder's surface area, radius, and height.

The formula for the surface area ( A ) of a cylinder is given by:

[

A = 2\pi r(h + r)

]

where:

• ( r ) is the radius,

• ( h ) is the height, and

• ( \pi ) is a constant approximately equal to 3.14.

Given the diameter of the cylinder is 95 cm, we can find the radius by dividing the diameter by 2:

[

r = \frac{95 \text{ cm}}{2} = 47.5 \text{ cm} = 0.475 \text{ m}

]

This conversion from cm to m is essential since the surface area is given in square metres.

Now, substituting the values into the surface area formula:

[

15 = 2\pi(0.475)(h + 0.475)

]

To isolate ( h ), first calculate the portion that involves ( \pi ):

[

15 = 2 \cdot 3.14