Carving a cone from a block — From a 10 × 5 × 2 cm block, a cone of radius 3 cm and height 7 cm is carved. What percentage of wood is wasted?

Introduction / Context:Waste percentage = (block volume − cone volume) / block volume * 100%. Use V_block = l * b * h and V_cone = (1/3)πr^2h.

Given Data / Assumptions:

• Block: 10 × 5 × 2 ⇒ V_block = 100 cm^3
• Cone: r = 3 cm, h = 7 cm

Concept / Approach:Compute cone volume exactly with π ≈ 22/7, then percentage waste.

Step-by-Step Solution:V_cone = (1/3) * π * 9 * 7 = 21π ≈ 65.973 cm^3Waste = 100 − 21π ≈ 34.027 cm^3Percentage waste ≈ 34.027%

Verification / Alternative check:Using π = 22/7 gives V_cone = 21 * 22/7 = 66 exactly; waste = 34/100 = 34%.

Why Other Options Are Wrong:46%, 54%, 66% are too large; 29% underestimates waste.

Common Pitfalls:Using diameter instead of radius or forgetting the 1/3 factor in cone volume.

Final Answer:34%