Find the volume of the cylinder. The slant height is 8 cm the length is 3 cm and the height is 6 cm
To find the volume of a cylinder, you can use the formula: V = πr^2h, where V is the volume, r is the radius, and h is the height.
To determine the radius, we can use the given information about the slant height. The slant height, the height, and the radius form a right triangle, with the slant height as the hypotenuse. Using the Pythagorean theorem, we can solve for the radius:
r^2 + h^2 = slant height^2
r^2 + 6^2 = 8^2
r^2 + 36 = 64
r^2 = 64 - 36
r^2 = 28
r = √28 ≈ 5.29 cm
Now that we have the radius, we can calculate the volume:
V = π(5.29 cm)^2(6 cm)
V ≈ 527.48 cm^3
Therefore, the volume of the cylinder is approximately 527.48 cm^3.