Question

A solid wooden cylindrical log of radius 35 cm and height 20 cm is used to make a glass holder box. 12 conical holes of height 15 cm and radius 3.5 cm are drilled into the upper surface of the log to accommodate glasses. The remaining upper surface area which is solid is covered with woolen cloth that costs Rs.4 per sq. cm and the inner surfaces of the holes are polished at the rate of Rs.0.25 per sq. cm. What is the total cost incurred ?

• A. Rs 14047
• B. Rs 15220
• C. Rs 15776.5
• D. Rs 16258

Answer 1

The Correct Option is A

Radius of the cylinder = 35 cm.
Hence the surface area of the upper surface of the cylinder = πr² = (22 ÷ 7) × 35² = (22 ÷ 7) × 1225 = 3850 cm²
Now, area of the surface which is not covered by the woolen cloth = number of holes X area of the circular base of each hole = 12 × πr² = 12 × (22 ÷ 7) × 3.5² = 462 cm²
Hence, area of the surface remaining = 3850 - 462 = 3388 cm²
The inside surface of the holes is the curved surface area of the conical holes.
Hence, Total C.S.A of the 12 holes =12 × π × 3.5 × 15 = 12 × (22 ÷ 7) × 3.5 × 15 = 1980 cm²
Therefore, Total cost = Cost of polishing + cost of covering with woolen cloth = 3388 × 4 + 1980 × 0.25 = Rs.14047
So, the correct option is (A) : Rs.14047.