Mathematics · Class 9-10

Surface Area and Volume (Mensuration)

Mensuration is the branch of geometry dealing with areas and volumes of two-dimensional and three-dimensional shapes. These concepts are essential for

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Why does the volume of a cone equal one-third of a cylinder with same radius and height?

This relationship can be verified by calculus or by experimental filling. A cone-shaped container holds exactly one-third the water of a cylindrical container with the same base radius and height.

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What is the difference between slant height and vertical height in a cone?

Vertical height is the perpendicular distance from the base to the apex. Slant height is the distance along the surface of the cone. They are related by the Pythagorean theorem: slant height squared equals radius squared plus vertical height squared.

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How do you find volume when only surface area is given?

Usually you need more information. If you know surface area and shape, you can set up equations. For example, if a cube has surface area 150 square cm, then 6a squared equals 150, so a squared equals 25 and a equals 5 cm, giving volume of 125 cubic cm.

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