Mathematics Kenya
Volume of solids
A group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation
Volume of solids
Volume of solids
Volume of a prism, a pyramid, a cone, a frustrum and a sphere
VOLUMS OF SOME THREE – DIMENSIONAL FIGURES
We have seen some formulas for calculating the surface areas of some three dimensional figures.
Let us see as well formulas for calculating the volumes of such figures.
-The amount of space that is enclosed by a space figure is called the volume.
The Volume is measured in cubic units, cubic meters (m3), Cubic centimeters (cm3) etc.When we find (calculate) the volume of a space figure or solid, we are finding the number ofcubic units enclosed by the given spaces figure.
(a) Volume of a Right Prism
The figure above shows a right rectangular prism. Let h be height, w width and ɭ the length of the prism.
Then the Volume of the prism is given by: V = Base area x height= ɭ×W×h
Generally, volume of any right prism is equal to the product of the area of the base and the height V = Base area x height.
(b) Volume of a Right Cylinder
Consider a right circular cylinder with radius” r “and height h as shown below.
The volume of a right circular cylinder is equal to the product of the area of the base and the height.
If V is volume, A is area of the base and h is the height,
Then Volume = Area of base x height
(c) Volume of a Pyramid
Generally, the volume of a pyramid is one – third the product of its altitude (height) and its base area.
If h is the perpendicular distance from the vertex of the pyramid to its base then,
(d)Volume of a Cone
Consider a cone of radius “r” and altitude h as shown below.
(e) Volume of a Sphere
The figure above shows a sphere of radius r, if the sphere can be put inside a cylinder of the same radius” r”, then the height h = 2r.
The Formulae to Calculate the Volume of Cylinders, Pyramids and Cones
Example 14
Find the volume of the prism shown below, given that the dimensions are in meters (m)
Example 15
Calculate the volume of a rectangular prism whose base is 8cm by 5cm and whose height is 10cm.
Example 16
Calculate the radius of a right circular cylinder of volume 1570m3 and height 20m. Use π=3.14
Example 17
A pipe made of metal 1cm thick, has an external (outside) radius of 6cm. Find the volume of metal used in making 4m of pipe. Use π=3.14
Example 18
Find the volume of a pyramid with rectangular base with length 6m and width 4m if the height of the pyramid is 10m.
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