Question

The diagram shows a right rectangular pyramid. If the volume of the pyramid is 80 cubic cm, calculate its heights in cm.

Answer 1

Hint: Start by letting the height of the pyramid be h. Use the formula that the volume of a pyramid is equal to one third of the base area multiplied by its height. Also, it is clear from the figure that the base of the pyramid is a rectangle and the area of the rectangle is the product of length and breadth.

Complete step-by-step answer:
Let us start the solution by knowing the structural property of a pyramid and drawing a representative diagram of it. In general the word pyramid refers to the ancient monuments built by the Egyptians to preserve the mummies but in actual the word pyramid refers to a polyhedron which consists of a polygon as its base and the triangles forming its side faces. The side faces meet at a single point called the apex of the pyramid. The side faces of the Pyramid are also called its lateral faces.
Now let us draw a diagram for better visualisation. Also, we let the height of the pyramid to be h cm.

Now, we know that the volume of a pyramid is equal to one third of the base area multiplied by its height. Also, it is clear from the figure that the base of the pyramid is a rectangle and the area of the rectangle is the product of length and breadth.
$\text{Volume of pyramid=}\dfrac{lbh}{3}$
$\text{80=}\dfrac{6\times 8\times h}{3}$
$\Rightarrow \dfrac{80\times 3}{6\times 8}=h$
$\Rightarrow h=5cm$
Therefore, the height of the pyramid as asked in the question is 5cm.

Note: You need to remember the formula of the volume of the pyramid and don’t get confused with the formula of the volume of the prism. As the formula of volume of the pyramid and the prism just differ by a factor of $\dfrac{1}{3}$ . Also, be careful in the calculation part and the units of the dimensions you are dealing with.