A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood.

### Concept & Volume of Material in a Cuboid The volume of the material (wood) used to make a hollow object is the difference between the external volume and the internal volume. $$ \text{Volume of Material} = \text{External Volume} - \text{Internal Volume} $$ ### Step-by-Step Solution 1. **Given:** Inner dimensions: $l = 115$ cm, $b = 75$ cm, $h = 35$ cm. Thickness $t = 2.5$ cm. It is a "covered" (closed) box. 2. **Calculate Outer Dimensions:** Since the box is closed, add $2t = 5$ cm to all inner dimensions. Outer length $L = 115 + 5 = 120$ cm. Outer breadth $B = 75 + 5 = 80$ cm. Outer height $H = 35 + 5 = 40$ cm. 3. **Calculate Volumes:** External Volume = $120 \times 80 \times 40 = 384000$ cu.cm. Internal Volume = $115 \times 75 \times 35 = 301875$ cu.cm. 4. **Calculate Volume of Wood:** $$ 384000 - 301875 = 82125 \text{ cu.cm} $$ ### Exam Strategy & Shortcut To quickly compute $115 \times 75 \times 35$, break it down or use digit sum/last digit logic if options are suitably spaced. Here, ending digits are 5, so exact calculation is safest. $115 \times 75 = 8625$, then $8625 \times 35 = 301875$. ### Common Pitfall Mistaking "inner measures" for outer measures and subtracting the thickness instead of adding it to find the missing dimensions. ### Final Answer Therefore, the correct answer is **82125 cu.cm**.