The volume of the rectangular block is 12288 m3. Its dimensions are in the ratio of 4 : 3: 2. If the entire surface is polished at the rate of 2 paise per m2,then find the total cost of polishing
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. ₹66.56.
Let the dimensions of the rectangular block be 4x, 3x, and 2x.
So, (4x) × (3x) × (2x) = 12288
⇒ 24x3 = 12288
⇒ x3 = 12288/24 = 512
⇒ x = ³√512 = 8
Length = 4x = 4 × 8 = 32 m; Width = 3x = 3 × 8 = 24 m; Height = 2x = 2 × 8 = 16 m
Surface area of a rectangular block = 2(lw + wh + lh)
= 2[(32 × 24) + (24 × 16) + (32 × 16)]
= 2(768 + 384 + 512)
= 2 × 1664
= 3328 m2
Total cost = 3328 × 2 = 6656 paise = ₹66.56
Therefore, the total cost of polishing the rectangular block is ₹66.56.