Question

Find the volume of a square based right prism whose base is 9 cm and height is 12 cm.

Answer 1

Hint: Find the area of the prism, which is equal to the area of the square. To find the volume, take the product of base area and height.

Complete step-by-step answer:
A square based right prism can also be called a right square prism. It is a box with at least one pair of opposite faces that are square. It can also be desired as a right prism with square bases. A right square prism which has a square lateral surface is a cube.
We can see the figure of a right square prism.

Let us consider ‘a’ as the side of the square. We have been given the side as 9 cm
$\therefore $Side of square \[=\ a\ =\ 9\ \text{cm}\]
Similarly, let us take height as ‘h’ marked in the figure i.e., \[h\ =\ 12\ \text{cm}\].
Now, Area of base of the prism \[=\] Area of the square \[=\] \[{{\left( \text{side} \right)}^{\text{2}}}={{a}^{2}}\]
i.e., Area of the base of the prism \[={{a}^{2}}\ =\ {{9}^{2}}\]
\[=9\times 9\ =\ 81\ c{{m}^{2}}\]
The volume of right prism \[=~\text{Base area}\times \text{height }=\ {{a}^{2}}\times h\]
\[=81\ c{{m}^{2}}\times h\]
\[=81\times 12\ =\ 972\ c{{m}^{3}}\]
Hence, we got the volume of the right square prism as \[972\ c{{m}^{3}}\].

Note: The volume of the right square prism \[={{a}^{2}}h\], which is a general formula.We can use it directly without thus much calculations. The lateral surface area of the same is given as \[4ah\].