Question

If a cubical shaped room has a volume of ′ a ′ m 3 , then find how much paint is required ( i n m 2 ) for the room except its base.

Answer 1

Given:

If a cubical shaped room has a volume of "a" m³.

To find:

How much paint is required ( in m 2 ) for the room except its base?

Solution:

To solve the given problem we will use the following formula:

• Volume of a cube = side³
• Total surface of cube = 6(side)²
• Area of a cube = (side)²

We are given that,

The volume of the cubical shaped room = a m³

∴ side³ = a

⇒ side = ∛a ← the length of each side of the cubical shaped room

Now, we are required to find the amount of paint required for the room except the base, so, we will find the area of the room

∴ The required amount of paint is,

= [Total Surface Area of the cubical room] - [Area of the base of the room]

= [6(side)²] - [side²]

substituting the value of side = ∛a

= [6(∛a)²] - [(∛a)²]

= 5(∛a)² m²

= $\bold{5a^\frac{2}{3} \:m^2}$

Thus, $\bold{\underline{5a^\frac{2}{3} \:m^2}}$ of paint is required for the room except for its base.

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