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

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

• A. 74.578
• B. 7.4578
• C. 745.78
• D. 0.7458

Answer: (B)

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

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