Question

Mensuration

b) The dimensions of a wall is 30 m x 5m x 20 cm. It contains three windows each
of 3m x 1.5 m. How many bricks of size 20 cm x 10 cm x 5 cm are required to
build the wall leaving 10% of the space for the cement work? Also find the cost of
bricks at the rate of Rs 9000 per 1000 bricks,​

Answer 1

`\boxed{\text{24 570 bricks; Rs221 130}}`

Explanation:

1. Number of bricks

(a) Volume of wall without windows

V = lwh = 30 m × 0.20 m × 5 m = 30 m³

(b) Volume of windows

One window: V = 1.5 m × 0.20 m × 3 m = 0.9 m³

Three window : V = 3 × 0.90 m³ = 2.7 m³

(c) Volume of wall with window openings

V = 30 m³ - 2.7 m³ =27.3 m³

(d) Volume of cement work

V = 0.10 × 27.3 m³ = 2.73 m³

(e) Volume of bricks

V = 27.3 m³ - 2.73 m³ =24.57 m³

(f) Volume of one brick

V = 0.20 m × 0.10 m × 0.05 m = 0.001 m³

(g) Number of bricks

`\text{No. of bricks} = \text{24 570 m}^(3) * \frac{\text{1 brick}}{\text{0.001 m}^(3) } = \textbf{24 570 bricks}\\\\\text{The wall will require } \boxed{\textbf{24 570 bricks}}`

2. Cost of bricks

`\text{Cost}= \text{24 570 bricks} *}\frac{\text{Rs9000}}{\text{ 1000 bricks}} = \text{Rs221 130 }\\\\\text{The cost of the bricks is } \boxed{\textbf{Rs221 130}}`