Mathematics Kenya
Volume of solids
Reading settings
Text size
Line spacing
Colours
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 1
Find the volume of the prism shown below, given that the dimensions are in meters (m)
Example 2
Calculate the volume of a rectangular prism whose base is 8cm by 5cm and whose height is 10cm.
Example 3
Calculate the radius of a right circular cylinder of volume 1570m3 and height 20m. Use π=3.14
Example 4
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 5
Find the volume of a pyramid with rectangular base with length 6m and width 4m if the height of the pyramid is 10m.
Listening to this topic
