Q: How do you find the height of a cone?

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It depends on what the cone looks like.

By means of Pythagoras' theorem providing you are given the radius and perpendicular height of the cone

Why do you need to FIND the slant height if you have the [lateral height and] slant height?

Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.

the slant height of a right circular cone is the distance from any point on the circle to the apex of the cone . The slant height of a cone is given by the formula ,√r2+h2 where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone.

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It depends on what the cone looks like.

you find the radius of a cone by the bottom of it or the round part

Volume of a cone = 1/3*pi*radius2*height

Cannot. If you do not know the angle of the cone, you cannot determine its height.

By means of Pythagoras' theorem providing you are given the radius and perpendicular height of the cone

Why do you need to FIND the slant height if you have the [lateral height and] slant height?

Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.

Volume formula for a cone: 1/3*pi*radius squared*height

the slant height of a right circular cone is the distance from any point on the circle to the apex of the cone . The slant height of a cone is given by the formula ,√r2+h2 where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone.

The height would be The square root of the square of the slant surface length minus the square of the radius of the cone at the base.

Volume of a cone = 1/3*pi*radius2*height