Question

A conference hall is 14 m long, 8 m wide and 4 m high. There are four windows and one
door in it. The door measures 1 m by 2 m and each window measures 1 m by 1.5 m.

(a) How many litres are needed to paint all the walls of the hall if one litre is enough for
covering 18 m??

(b) What will be the cost of painting the hall if 1 litre costs 7 225?​

Answer 1

Given :-

• A conference hall, Length = 14 m, Breadth = 8 m and Height = 4 m.

• There are four windows and one door in there which measures 1m by 1.5 m and 1 m by 2 m respectively.

To Find :-

• How many Litres needed to paint all the walls if 1 Litre is enough to paint 18m².

• Cost of painting the hall, if 1 Litre costs ₹ 225.

Solution :-

It is clear that we won't paint the doors and windows so we need to find the surface area of the walls excluding the 4 windows and one door.

Since, the hall is in the form of a cuboid, So

⇒ Total Surface Area = 2(LH + BH + BL)

Where,

• L = length
• B = breadth
• H = height

⇒ TSA of Hall = 2(14×4 + 8×4 + 14×8)

⇒ TSA of Hall = 2( 56 + 32 + 112 )

⇒ TSA of Hall = 2( 88 + 112 )

⇒ TSA of Hall = 2 × 200

⇒ TSA of Hall = 400 m²

Now, We need to subtract the surgace area of four windows and one door from it.

⇒ Area = TSA of Hall - (Area of 4 windows + Area of one door)

⇒ Area = 400 - (4×1.5×1 + 2×1)

⇒ Area = 400 - (6 + 2)

⇒ Area = 392 m²

Given that, 18m² can be painted with 1 L.

⇒ Amount of paint = Area / 18

⇒ Amount of paint = 392 / 18

⇒ Amount of paint = 21.78 L

Now, The rate is given as ₹ 225 per litre.

So,

⇒ Cost = 225 × 21.78

⇒ Cost = ₹ 4900.5

Answer 2

Answer:

Step-by-step explanation:

(a)

We have,

Length = 14 m.

Breadth = 8 m.

Height = 4 m.

(i) Area of 4 walls of the hall = 2h(l + b)

                                              = 2 * 4(14 + 8)

                                              = 176 m²

(ii)

Area of 1 door = 2 m².

Area of 1 window = 1.5 m²

∴ Area of 4 windows = 4 * 1.5

                                   = 6 m²

∴ Area of four walls to be painted

= [176 - (2 + 6)]

                                       = 176 - 8

                                      = 168 m²

Given that one litre is enough for covering 18 m².

Then, cost of painting 168 m² = (168/18)

                                = 28/3

                               = 9(1/3) litres.

(b)

1 litre = 225

9(1/3) litres = ?

⇒ (225 * 28)/3

⇒ 6300/3

⇒ 2100.

Therefore, cost of painting is 2100.