Question

The diagram shows a pyramid whose base is a regular pentagon of area \[42c{{m}^{2}}\] and whose height is 7cm. What is the volume of the pyramid?

Answer 1

Hint: In this problem, we have to find the volume of the pyramid, whose base is a regular pentagon of area \[42c{{m}^{2}}\] and whose height is 7cm. We know that the formula for the volume of a pyramid is \[V=\dfrac{1}{3}\times A\times h\]. We know that we are already given the area of the base and the heigh, which we have to substitute in the formula, to get the answer.

Complete step by step answer:
We are given a pyramid whose base is a regular pentagon of area \[42c{{m}^{2}}\] and whose height is 7cm.

We have to find the volume of the pyramid.
We know that the formula for the volume of the pyramid is,
Volume of Pyramid, \[V=\dfrac{1}{3}\times A\times h\].
Where, A is the area of the base and h is the Height.
We can now substitute the given values in the above formula, we get
\[\Rightarrow V=\dfrac{1}{3}\times 42\times 7\]
We can now simplify the above step, we get
\[\Rightarrow V=98c{{m}^{3}}\]

Therefore, the volume of the pyramid whose base is a regular pentagon of area \[42c{{m}^{2}}\] and whose height is 7cm is \[98c{{m}^{3}}\].

Note: Students make mistakes while writing the formula for the volume of the pyramid, which is \[V=\dfrac{1}{3}\times A\times h\]. We should also remember that we have to write the unit whenever we write the final answer. We should also remember that the unit of volume is in cubic units.