The volume of air inside a hall with a square floor and height 15 m is 1500…
2026
The volume of air inside a hall with a square floor and height 15 m is 1500 m3. What is the maximum length of a log that can be placed diagonally inside the hall? Give the answer correct to two decimal places.
Answer: D. 20.62 m — ConceptFor a cuboid of length l, breadth b, and height h, the volume is V = lbh. The longest straight segment that fits inside a cuboid is its space diagonal,…
- A.
25.45 m
- B.
28.75 m
- C.
27.08 m
- D.
20.62 m
Attempted by 9 students.
Show answer & explanation
Correct answer: D
Concept
For a cuboid of length l, breadth b, and height h, the volume is V = lbh.
The longest straight segment that fits inside a cuboid is its space diagonal, d = √(l2 + b2 + h2).
Application
Let the side of the square floor be s. Since V = s2h, s2 = 1500 ÷ 15 = 100, so s = 10 m.
The hall therefore has dimensions 10 m × 10 m × 15 m.
Using the space-diagonal formula, d = √(102 + 102 + 152) = √(100 + 100 + 225) = √425.
Thus d = 20.6155… m, which rounds to 20.62 m to two decimal places.
Cross-check
The exact squared diagonal is 425 m2. Also, 20.622 = 425.1844; the small difference is caused only by rounding to two decimal places.
Result
The maximum length of the log is 20.62 m.