Question

The surface area of a cylinder is given by the formula SA = 2r2 2rh. A cylinder has a radius of 8 cm and a surface area of 688 cm2 . Find the height of the cylinder.

Answer 1

To find the height of the cylinder, we can use the given surface area formula and substitute the known values.

The surface area formula for a cylinder is SA = 2πr^2 + 2πrh, where "SA" represents the surface area, "r" represents the radius, and "h" represents the height of the cylinder.

In this case, we are given that the radius (r) is 8 cm and the surface area (SA) is 688 cm^2.

Let's substitute these values into the formula:

688 = 2π(8^2) + 2π(8h)

To simplify, we can use the value of π as approximately 3.14:

688 = 2(3.14)(8^2) + 2(3.14)(8h)

Simplifying further:

688 = 2(3.14)(64) + 2(3.14)(8h)

688 = 402.88 + 50.24h

Next, we can isolate the term with the height:

688 - 402.88 = 50.24h

285.12 = 50.24h

Now, divide both sides of the equation by 50.24:

h = 285.12 / 50.24

h ≈ 5.67 cm

Therefore, the height of the cylinder is approximately 5.67 cm

Explanation: