Question

A hall is 10 m long, 5 m wide and 4 m high. It has one door 2 m by 1 m and 2 windows 1 m by 80 cm. Find the

1. area of the 4 walls (excluding the door and windows).
2. cost of distempering the walls at ₹ 50 per m².
3. cost of polishing the floor at the rate of ₹ 5 per m².

Answer 1

Given:

• Hall dimensions: length = 10 m, width = 5 m, height = 4 m
• Door dimensions: 2 m by 1 m
• Window dimensions: 1 m by 80 cm (0.8 m) and there are 2 such windows
• Cost of distempering = ₹ 50 per m²
• Cost of polishing floor = ₹ 5 per m²

i. Area of the 4 walls (excluding the door and windows)

Step 1: Calculate total area of 4 walls

Walls consist of two lengths and two widths:

Area of 4 walls = 2 × height × (length + width)

= 2 × 4 × (10 + 5)

= 2 × 4 × 15

= 120 m²

Step 2: Calculate area of door and windows

Door area = 2 × 1 = 2 m²

Window area for one window = 1 × 0.8 = 0.8 m²

For 2 windows = 2 × 0.8 = 1.6 m²

Total door and window area = 2 + 1.6 = 3.6 m²

Step 3: Calculate wall area excluding door and windows

Excluding area = 120 − 3.6 = 116.4 m²

ii. Cost of distempering the walls at ₹ 50 per m²

Cost = Area to be distempered × Rate per m²

= 116.4 × 50

= ₹ 5820

iii. Cost of polishing the floor at the rate of ₹ 5 per m²

Floor area = length × width

= 10 × 5

= 50 m²

Cost = Floor area × Rate per m²

= 50 × 5

= ₹ 250

Area of 4 walls (excluding door and windows) = 116.4 m²

Cost of distempering walls = ₹ 5820

Cost of polishing floor = ₹ 250