What is the height of a cylinder with a surface area of 10 square metres and a diameter of 75 cm?

To find the height of the cylinder with a given surface area and diameter, we start by recalling the formula for the surface area of a cylinder, which is:

[

\text{Surface Area} = 2\pi r(h + r)

]

Here, ( r ) is the radius, ( h ) is the height, and ( \pi ) is a constant (approximately 3.14).

First, we need to convert the diameter from centimeters to meters since the surface area is given in square meters. The diameter is 75 cm, which translates to 0.75 meters. Therefore, the radius ( r ) is half of the diameter:

[

r = \frac{0.75}{2} = 0.375 \text{ m}

]

Now, substituting the values we know (surface area = 10 m² and radius = 0.375 m) into the surface area formula:

[

10 = 2\pi (0.375)(h + 0.375)

]

To simplify, we compute the term ( 2\pi(0.375) ):

[

2\pi(0.375) \approx