A cube is a three-dimensional figure with six matching square sides.
The figure above shows a cube. The dotted lines indicate edges hidden from your view.
If s is the length of one of its sides, then the volume of the cube is s × s × s
Volume of the cube = s3
A rectangular solid is also called a rectangular prism or a cuboid.
In a rectangular solid, the length, width and height may be of different lengths.
The volume of the above rectangular solid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. The other faces are in the shape of rectangles. They are called lateral faces.A prism is named after the shape of its base.
When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.
The volume of a right prism is given by the formula:
Volume of prism = Area of base × length
V = Al
where A is the area of the base and l is the length or height of the prism.
A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.
The volume of a cylinder is given by the formula:
V = π r2h
where r = radius of cylinder and h is the height or length of cylinder.
Sometimes you may be required to calculate the volume of a hollow cylinder or tube.
Volume of hollow cylinder
where R is the radius of the outer surface and r is the radius of the inner surface.
A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex.
The volume of a cone is given by the formula:
Volume of cone = Area of base × height
V = where r is the radius of the base and h is the height of the prism.
A pyramid is a solid with a polygonal base and several triangular lateral faces. The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. The pyramid is named after the shape of its base. For example a rectangular pyramid or a triangular pyramid.
The volume of a pyramid is given by the formula:
Volume of pyramid = Area of base × height
V = where A is the area of the base and h is the height of the pyramid.
A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The distance from the center to the surface is the radius.
Volume of sphere = where r is the radius.
A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.
Volume of hemisphere where r is the radius
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