DAV Class 8 Maths Chapter 14 Value Based Questions

Mensuration Value Based Questions

1. Raman, a painter, always donated one-fifth of his income to an orphanage. He got a contract of painting a house having three rooms of dimensions 10 m × 12 m × 3.5 m, 8 m × 6 m × 3.5 m and 7 m × 5 m × 3.5 m. He charged ₹ 30 per m² for his work.

(a) How much money did Raman earn?

Solution

Room 1	Room 2	Room 3
l = 10m b = 12m h = 3.5m	l = 8m b = 6m h = 3.5m	l = 7m b = 5m h = 3.5m

\[ \begin{aligned} \text{Area to be painted} &= \color{green} \text{Area of 4 walls} + \text{Ceiling area} \\ &= \color{green} [2 \times (l + b) \times h] + (l \times b)\\ \\ \text{Area of Room } 1: & = [2 \times (10+12) \times 3.5] + (10 \times 12) \\ &= (7 \times 22) + 120 \\ &= 154 + 120 \ \text{m}^2 \\ &= 274 \ \text{m}^2 \\ \\\text{Area of Room } 2: & = [2 \times (8 + 6) \times 3.5] + (8 \times 6) \\ &= (7 \times 14) + 48 \\ &= 98 + 48 \ \text{m}^2 \\ &= 146 \ \text{m}^2 \\ \\\text{Area of Room } 3: & = [2 \times (7 + 5) \times 3.5] + (7 \times 5) \\ &= (7 \times 12) + 35 \\ &= 84 + 35 \ \text{m}^2 \\ &= 119 \ \text{m}^2 \\ \\\text{Total area} &= 274 + 146 + 119 \\ &= 539 \ \text{m}^2 \\[6pt] \text{Cost} &= \text{₹ }30 \text{ per m}^2 \\[2pt] \color{green}{\text{Earnings}} &= 539 \times 30 \\ &= \text{₹ } 16170 \end{aligned} \]

Answer Raman earned \( \color{red}{\text{₹ } 16170 }\)

(b) Find the amount of money he gave to the orphanage.

Solution

\[ \begin{aligned} \text{Donation} &= \frac{1}{\cancel5_1} \times \cancel{16170}^{3234} \\ \\ \implies & \text{₹ } 3234 \end{aligned} \]

Answer Amount donated \(=\ \color{red}{\text{₹ } 3234}\)

Answer Caring.

2. For ‘Beti Bachao, Beti Padhao’, a rally was organised by a school. Monal wrote the slogan on a trapezium-shaped cardboard having the length of parallel sides \(60\) cm and \(90\) cm and the distance between them \(50\) cm.

(a) Find the area of the trapezium.

Solution

\[ \begin{align*} a &= 57 \, \text{cm} \\ b &= 33 \, \text{cm} \\ h &= 13 \, \text{cm} \\ \\ \color{green} \text{Area of the trapezium} &= \color{green} \frac{1}{2} \times (a + b) \times h \\[6pt] &= \frac{1}{2} \times (60 + 90) \times 50 \\[6pt] &= \frac{1}{{\cancel{2}}_{\color{green}1}} \times {{\cancel{150}}^{\color{green}75}} \times 50 \\[6pt] &= 75 \times 50 \\[6pt] \text{Area} &= 3750 \, \text{cm}^2 \end{align*} \]

Answer Area of the trapezium \(=\ \color{red}{3750\ \text{cm}^2}\)

(b) What are your views about girl education?

Answer Girl education is must.

Answer Encourage people to send girls to school.