Question

John is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 cm , 10 cm

and 7 cm respectively. from each can he can paint 100 cm² area . how many cans of paints will he need to

paint the rrom ?​

Answer 1

Given:

✰ Length of a cuboidal hall = 15 cm

✰ Breadth of a cuboidal hall = 10 cm

✰ Height of a cuboidal hall = 7 cm

✰ Area can be painted by each can = 100 cm²

To find:

✠ How many cans of paints will he need to paint the room ?

Solution:

Let's understand the concept first! First we will find area of the walls and the ceiling. To find the area of the walls and the ceiling, we will subtract the area of the floor from the total surface area. We will find total surface area and area of floor by using respective formulas for both. Then, we are provided with the area can be painted by each can, using it we will find the number of cans needed to paint the room.

Let's find out...✧

Formula used:

✭ Total surface area = 2( lb + bh + hl ) ✭

Here,

• l is the length of a cuboidal hall.
• b is the breadth of a cuboidal hall.
• h is the height of a cuboidal hall.

✭ Area of floor = l × b ✭

Here,

• l is the length of a cuboidal hall.
• b is the breadth of a cuboidal hall.

Now,

➛ Area of walls and ceiling = Total surface area - Area of floor.

➛ Area of walls and ceiling = 2( lb + bh + hl ) - ( l × b )

Putting the values,

➛ Area of walls and ceiling = 2( 15 × 10 + 10 × 7 + 7 × 15 ) - ( 10 × 15 )

➛ Area of walls and ceiling = 2 ( 150 + 70 + 105 ) - ( 150 )

➛ Area of walls and ceiling = 2 ( 220 + 105 ) - ( 150 )

➛ Area of walls and ceiling = 2 ( 325 - 150 )

➛ Area of walls and ceiling = 650 - 150

➛ Area of walls and ceiling = 500 cm²

Then,

➤ Number of cans of paint needed = Area of walls and ceiling/Area can be painted by each can

➤ Number of cans of paint needed = 500/100

➤ Number of cans of paint needed = 5

∴ 5 cans of paints he will need to paint the room.

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Answer 2

Given :

• Length of Room = 15cm
• Breadth of Room = 10cm
• Height of Room = 7cm
• Area painted by 1 can = 100cm²

To Find :

• Total Number of Cans required to paint the walls and the ceiling.

Solution :

✰ In this question, Firstly we will find the Area of the 4 walls after that we will find the Area of the ceiling now after getting both the Areas we will add them to get the Total Area of the Room to be painted and we know that Area of 4 walls is given by 2(Length + Breadth) and Area of ceiling is given by Length × Breadth . Now Total Number of Cans required to paint the walls and the ceiling will be given be Total Area of Room/Area painted by 1 can .

⠀

Area of 4 walls :

⟶⠀Area = 2(Length + Breadth) Height

⟶⠀Area = 2(15 + 10) × 7

⟶⠀Area = 2 × 25 × 7

⟶⠀Area = 25 × 14

⟶⠀Area = 350cm²

⠀

___________________

Area of Ceiling :

⟶⠀Area = Length × Breadth

⟶⠀Area = 15 × 10

⟶⠀Area = 150cm²

⠀

___________________

Total Area to be Painted :

⟶⠀ Area of 4 walls + Area of Ceiling

⟶⠀ 350 + 150

⟶⠀ 500cm²

⠀

___________________

Number of Cans Required :

⟶⠀ Total Area/Area painted by 1 can

⟶⠀ 500/100

⟶⠀ 5 cans

⠀

So, 5cans will be required to paint the walls and the ceiling of the room.

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