Question

What is the volume of this cone?

Answer 1

c = 490/3

Explanation:

Answer 2

The volume of the cone is approximately 453.0 cm³

Explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

`a^2 = b^2 + c^2`

So we can find the height of the cone with that:

`10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = √(61.88)\\h \approx 7.9`

Now that we have the cone's height, we can solve for its volume:

`v = (1)/(3) \pi r^2 h\\v = (1)/(3) \pi * 7.4^2 * 7.9\\v = (1)/(3) \pi * 54.76 * 7.9\\v = (1)/(3) \pi * 432.6\\v = \pi * 144.2\\v \approx 453.0 cm^3`