How do I find the volume of a cylinder with a height of 5cm and the diagonal of 13cm?

Answer 1

When you say diagonal do you mean from a point on the circumference at one end to the opposite point on the circumference at the other end? If so then:

Diameter of the end can be calculated using Pythagoras:

diameter = √(13² - 5²) = √144 = 12

radius = ½ diameter = ½ × 12 = 6

volume cylinder = π × radius² × height = π × 6² × 5 = 180π cm³ ≈ 565.5 cm³

Answer 2

You first figure out the radius - if I understand the question correctly, you can find out the diameter using the Pythagorean theorem. The radius is half the diameter. Then you can use the standard formula for the volume of a cylinder.

Answer 3

h = 5 cm, diag = 13 cm therefore, by Pythagoras, diameter = sqrt(13^2 - 5^12) = 12 cm.So radius = 6 cm.

Then volume = oi*r^2*h = 565.5 cm^3.