Question

Water in a canal, 6 m wide and 2 m deep, is flowing with the speed of 18 km/h.

Statement (1): The volume of water that flows through the canal in 20 minutes \[ =6 \times 2 \times\left(18 \times \frac{5}{18}\right) \times 20 \times 60 \mathrm{~m}^{3}\]

Statement (2): The volume of water that flows through the canal = 6 × 2 × 18 × 20 m³.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is true, and statement 2 is false.

Explanation:

Given, water in a canal 6 m wide and 2 m deep, is flowing with the speed of 18 km/h.

Volume of water flowing through the canal = Area of cross-section × speed × time

Area of cross-section = width × depth \[= (6 \times 2)\ \text{m}^2\]

Speed \[= 18\ \text{km/h} = 18 \times \frac{1000}{3600} = \left(18 \times \frac{5}{18}\right)\ \text{m/sec}\]

Time \[= 20\ \text{minutes} = 20 \times 60\ \text{sec}\]

∴ Volume \[= 6 \times 2 \times 18 \times \frac{5}{18} \times 20 \times 60\ \text{m}^3\]

Thus, Statement 1 is true, and statement 2 is false.