Question

The volume of air in a room $10m$ long, $6.5m$ wide, and $5m$ height is:
A) $425{\text{ cube m}}$
B) $225{\text{ cube m}}$
C) $325{\text{ cube m}}$
D) ${\text{None of the above}}$

Answer 1

Hint:
A room is in the shape of a cuboid, the volume of air in the room can find out by finding the volume of a cuboid having a length, width and height as given in the question using the formula of volume of a cuboid, \[{\text{Volume of Cuboid = }}\left( {{\text{Length}} \times {\text{Width}} \times {\text{Height}}} \right)\]. As air is present in the complete room so if we can find the volume of the room which is in the cubical form will give us the required answer.

Complete step by step solution:
We will first consider the given dimensions of the room that is ${\text{L}} = 10m,{\text{ W}} = 6.5m,{\text{ H}} = 5m$ .
Next, we need to find the volume of air present in the room so, if we find the volume of cuboid we are done.
Thus, to find the volume of air in the room, we will have to find the volume of the room.
Here, the formula of cuboid, \[{\text{Volume of Cuboid = }}\left( {{\text{Length}} \times {\text{Width}} \times {\text{Height}}} \right)\]is used because the shape of room is cuboid.
Thus, we get,
\[
   \Rightarrow {\text{Volume of Cuboid = }}\left( {{\text{Length}} \times {\text{Width}} \times {\text{Height}}} \right) \\
   \Rightarrow {\text{Volume of Cuboid = }}\left( {10 \times 6.5 \times 5} \right){\text{ cube m}} \\
   \Rightarrow {\text{Volume of Cuboid = 325 cube m}} \\
 \]
So, the volume of air in the room is $325{\text{ cube m}}$.

Hence, option C is the correct answer which is $325{\text{ cube m}}$.

Note:
Volume of air in the room is equal to the volume of room as air is present in a full room. As the room is in cuboid shape so we have applied the formula of volume of a cuboid. The units are the same of all the dimensions so, no need to change the units. The values of length, width and height are given so we have directly done the substitution of values in the formula. Do remember the formula for the volume of a cuboid.