Volume of prisms
Watch this video to learn how to calculate the volume of prisms and cylinders.
A prism is a solid with a uniform A shape or surface that is shown as the result of cutting through it in half, so that the inside can be seen, eg a cross-section of a river or of a mathematical shape.. This means that no matter where it is sliced along its length, the cross section is the same size and shape (congruent).
A well-known example of a prism is a cylinder and you can see from the image above that the front face (cross-section) is the same size of circle no matter where you slice it.
\(V = Ah\)
Question
Calculate the volume of the prism.
\(V = Ah\)
\(= 54 \times 12\)
\(= 648c{m^3}\)
Question
Calculate the volume of the prism.
This shape is a triangular prism so the area of the cross-section is the area of a triangle.
Area of the triangle:
\(A = \frac{1}{2}bh\)
\(= \frac{1}{2} \times 6 \times 4\)
\(= 12c{m^2}\)
Volume of the prism:
\(V = Ah\)
\(= 12 \times 12\)
\(= 144c{m^3}\)
Volume of a cylinder
The formula for the volume of a cylinder (circular prism) is derived from the volume of a prism, where \(r\) is the radius and \(h\) is the height/length.
\(V = Ah\)
Since the area of a circle \(= \pi {r^2}\), then the formula for the volume of a cylinder is:
\(V = \pi {r^2}h\)
Question
Calculate the volume of the cylinder shown.
Give your answer correct to 1 Giving a number to a specified number of significant figures is a method of rounding. For example, in the number 7483, the most significant, or important, figure is 7, as its value is 7000. To give 7483 correct to one significant figure (1 sf), would be 7000. To 2 sf, it would be 7500..
\(V = \pi {r^2}h\)
\(= \pi \times {4^2} \times 10\)
\(= 502.654...\)
\(= 500c{m^3}\,(to\,1\,s.f.)\)
