Question

the volume of a room is 120m^3 and the area of its floor is 30 m ^2 find the height of the room​

Answer 1

Answer :

›»› The height of the room is 4 m.

Step-by-step explanation :

Given :

• The volume of a room = 120 m³.
• The area of its floor = 30 m².

To Find :

• The height of the room = ?

Solution :

Since room is always is in the shape of cuboid, and floor is always is in the shape of rectangle.

As we know that

→ Volume of cuboid = length * breadth * height.

→ Area of rectangle = length * breadth.

Let us assume that, the height of a room is x m.

According to the given question,

→ Volume of room = Area of floor * height

→ 120 = 30 * x

→ 120 = 30x

→ x = 120/30

→ x = 12/3

→ x = 4

Hence, the height of the room is 4 m.

Verification :

→ Volume of room = Area of floor * height

→ 120 = 30 * 4

→ 120 = 120

Clearly, LHS = RHS.

Here both the conditions satisfy, so our answer is correct.

Hence Verified !

Answer 2

$\huge \bf \underbrace {Given}$

• Volume of room = 120 m³
• Area of floor = 30 m²

$\huge \bf \underbrace {To \: Find}$

Height of room

$\huge \bf \underbrace {Formula}$

1. Volume = length × breadth × height
2. Area = Length × Breadth

$\huge \bf \underbrace {Solution}$

Let the height be a

Here,

Volume and area is given

And we have to find its height

$\sf \: volume \: of \: room \: = area \: of \: room$

$\sf {length}\: \times \: breadth = length \: \times breadth \times height$Here,

Length and breadth will be cancelled from both sides.

Therefore

$\sf \: 120 = 30 \times a$

$\sf \: 120 = 30a$

$\sf \: a = \dfrac{120}{30}$

$\sf \: a \: = 4$

Hence :-

The height of the room is 4 m