Question

If a regular square pyramid has a base of side 8 cm and height of 30 cm, then its volume is
(a) 120 cc
(b) 240cc
(c) 640 cc
(d) 900cc

Answer 1

Hint: We will apply the formula to find the volume of the pyramid which is given by $\text{volume of the pyramid = }\dfrac{\text{1}}{3}\text{ }\!\!\times\!\!\text{ area of square base }\!\!\times\!\!\text{ height}$ where the area of the square base will be the area of the square only. The area of the square is ${{\left( \text{side} \right)}^{\text{2}}}$.

Complete step-by-step answer:

The diagram for the given question is given below.

Here we can clearly see that the above diagram is of a pyramid. And this pyramid consists of a square base.
As we are supposed to find the volume of the pyramid therefore, for that we will first find its surface area of the base. This can be done by the formula of area of a square given by $\text{side}\times \text{side}$. As the side of the square base ABCD is given as 8 cm Thus, we get
 $\begin{align}
  & \text{area of the square base = 8 cm}\times \text{8 cm} \\
 & \Rightarrow \text{area of the square base = 64 c}{{\text{m}}^{2}} \\
\end{align}$
As the base is now an area of square and height is given to us as 30 cm. Therefore, the $\text{volume of the pyramid = }\dfrac{\text{1}}{3}\text{ }\!\!\times\!\!\text{ area of square base ABCD }\!\!\times\!\!\text{ height}$
So, by substituting the values in the above formula we will get,
$\begin{align}
  & \text{volume of the pyramid = }\dfrac{\text{1}}{3}\text{ }\!\!\times\!\!\text{ area of square base ABCD }\!\!\times\!\!\text{ height} \\
 & \Rightarrow \text{volume of the pyramid = }\dfrac{\text{1}}{3}\text{ }\!\!\times\!\!\text{ 64 c}{{\text{m}}^{2}}\text{ }\times \text{30 cm} \\
 & \Rightarrow \text{volume of the pyramid = 64 c}{{\text{m}}^{2}}\text{ }\times 10\text{ cm} \\
 & \Rightarrow \text{volume of the pyramid = }640\text{ c}{{\text{m}}^{3}} \\
\end{align}$
Hence the volume of the pyramid is 640 cubic centimetres.
Therefore, we have got the correct answer as option (c) 640c.c.

Note: One can mistake in using the formula for of area of the triangle is $\dfrac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ base }\!\!\times\!\!\text{ height}$ instead of the pyramid. Since, the pyramid and triangle looks similar but the triangle is a two dimensional figure while a pyramid is a three dimensional figure. In three dimensional a triangle changes into a prism. Also, the volume of a prism and volume of the pyramid are also different as the volume of pyramid is given by the formula $\text{volume of the pyramid = }\dfrac{\text{1}}{3}\text{ }\!\!\times\!\!\text{ area of square base ABCD }\!\!\times\!\!\text{ height}$ and volume of prism is given by $\text{area of prism = }\dfrac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ base }\!\!\times\!\!\text{ height }\!\!\times\!\!\text{ thickness}$. While solving the question one should first check whether the units of the segments of the pyramid are same or different. In case they are different we need to change them into the same units.