The volume of rectangular block is 12288 m³. Its dimension are in the ratio of 4 : 3: 2. If the entire surface is polished at the rate 2 paise per m²,then find the total cost of polishing

Given:

Volume of the rectangular block = 12288 m³

Dimensions ratio = 4 : 3 : 2

Rate of polishing = 2 paise per m²

Formula used:

Volume = length × breadth × height

Total Surface Area = 2(lb + bh + hl)

Total Cost of Polishing = Total Surface Area × Rate of Polishing

Calculation:

Let the dimensions be 4x, 3x, and 2x

Volume = 4x × 3x × 2x

⇒ 24x³ = 12288

⇒ x³ = 12288 / 24

⇒ x³ = 512

⇒ x = 8

Dimensions: 4x = 4 × 8 = 32 m, 3x = 3 × 8 = 24 m, 2x = 2 × 8 = 16 m

Total Surface Area = 2(lb + bh + hl)

⇒ Total Surface Area = 2(32 × 24 + 24 × 16 + 16 × 32)

⇒ Total Surface Area = 2(768 + 384 + 512)

⇒ Total Surface Area = 2(1664)

⇒ Total Surface Area = 3328 m²

Total Cost of Polishing = Total Surface Area × Rate of Polishing

⇒ Total Cost of Polishing = 3328 × 2

⇒ Total Cost of Polishing = 6656 paise

Convert paise to rupees:

⇒ Total Cost of Polishing = 6656 / 100

⇒ Total Cost of Polishing = Rs. 66.56

∴ The correct answer is option (3).