The length, breadth and height of a rectangular box are in the ratio o

1.	The length, breadth and height of a rectangular box are in the ratio of 3 : 2 : 4 respectively and the cost of covering it with a sheet of paper at the rate of Rs. 1.50 per square metre is Rs. 1,950. Find the volume of the box.1. 2000 m32. 3200 m33. 3000 m34. 3500 m3
Answer» Correct Answer - Option 3 : 3000 m³ Given: The length, breadth and height of a rectangular box are in the ratio of 3 : 2 : 4 respectively Cost of covering it at the rate of Rs. 1.50 per square metre = Rs. 1,950 Formula used: The total surface area of a rectangular box = 2 (length × breadth + breadth × height + height × length) The volume of a rectangular box = length × breadth × height Calculation: Let the length, breadth and height of a rectangular box be 3x, 2x and 4x respectively. The total surface area of a rectangular box = 2[(3x × 2x) + (2x × 4x) + (4x × 3x)] ⇒ 2 × (6x² + 8x² + 12x²) ⇒ 2 × 26x² ⇒ 52x² Total cost for covering it at the rate of Rs. 1.5 per square metre = Rs. 1,950 ⇒ 52x² × 1.5 = 1,950 ⇒ x² = 1950/(52 × 1.5) ⇒ x² = 25 ⇒ x = 5 metres Then, length = 3x ⇒ 3 × 5 ⇒ 15 metres Breadth = 2x ⇒ 2 × 5 ⇒ 10 metres Height = 4x ⇒ 4 × 5 ⇒ 20 metres The volume of a rectangular box = 15 × 10 × 20 ⇒ 3000 m³ ∴ The volume of rectangular box is 3000 m³

The length, breadth and height of a rectangular box are in the ratio of 3 : 2 : 4 respectively and the cost of covering it with a sheet of paper at the rate of Rs. 1.50 per square metre is Rs. 1,950. Find the volume of the box.1. 2000 m32. 3200 m33. 3000 m34. 3500 m3

Answer» Correct Answer - Option 3 : 3000 m³

Given:

The length, breadth and height of a rectangular box are in the ratio of 3 : 2 : 4 respectively

Cost of covering it at the rate of Rs. 1.50 per square metre = Rs. 1,950

Formula used:

The total surface area of a rectangular box = 2 (length × breadth + breadth × height + height × length)

The volume of a rectangular box = length × breadth × height

Calculation:

Let the length, breadth and height of a rectangular box be 3x, 2x and 4x respectively.

The total surface area of a rectangular box = 2[(3x × 2x) + (2x × 4x) + (4x × 3x)]

⇒ 2 × (6x² + 8x² + 12x²)

⇒ 2 × 26x²

⇒ 52x²

Total cost for covering it at the rate of Rs. 1.5 per square metre = Rs. 1,950

⇒ 52x² × 1.5 = 1,950

⇒ x² = 1950/(52 × 1.5)

⇒ x² = 25

⇒ x = 5 metres

Then, length = 3x

⇒ 3 × 5

⇒ 15 metres

Breadth = 2x

⇒ 2 × 5

⇒ 10 metres

Height = 4x

⇒ 4 × 5

⇒ 20 metres

The volume of a rectangular box = 15 × 10 × 20

⇒ 3000 m³

∴ The volume of rectangular box is 3000 m³