Surface Areas and Volumes

In our daily life we may come across various solids that are made by a combination of one or more solid objects, like an ice-cream cone, capsule, toy etc. Surface Area of a Combination of Solids Surface area is the measure of exposed area of an object. It is expressed in square units.To find the surface area of a combination of a solid, we have to add all the visible surfaces areas of the combined solid. The surface area of a solid, which is made up of a cylinder with two hemispheres at either end is the sum of the curved surface areas of the cylinder and both the hemispheres. The surface area of a solid, which is made up of a cone and a hemisphere is the sum of the curved surface areas of the cylinder and the cone. Volume of a Combination of Solids Volume of a solid object is the space occupied by the solid. The volume of a combined solid is equals to the sum of volumes of the basic solids used to form the combined solid. Volume a solid obtained by the removing a shape from it, is equal to the volume of original solid minus volume of the removed shape. Conversion of Solids When one solid is converted into another solid having a different shape, it is called conversion of solids. Volume of the converted solid is equal to the volume of the original solid. Frustum of a Cone If a plane cuts off a right circular cone parallel to its base, then the portion of the cone between the cutting plane and the base of the cone is called the frustum of the cone. h = vertical height of the frustum, R and r are radii of the two bases (ends) of the frustum. h = vertical height of the frustum, R and r are radii of the two bases (ends) of the frustum. h = vertical height of the frustum, R and r are radii of the two bases (ends) of the frustum.

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