Question

A cube (10 × 10 × 10) intersects coaxially with a truncated cone (base diameter 12, top diameter 6, height 11). The cube then vanishes along with the part of the truncated cone inside it. What remains?

• A. A
• B. B
• C. C
• D. D

Hint:

When solids intersect and one vanishes, the remaining solid carries the “negative imprint” of the vanished solid’s volume.

Answer 1

The Correct Option is D

Step 1: Understand the geometry.
The truncated cone has a circular base (diameter 12) and is coaxial with the cube (10 × 10 × 10). When both are aligned on the same base, the cube cuts out a central cylindrical volume from the cone.
Step 2: What happens when cube vanishes?
The cube is removed along with the intersected portion of the cone. This means that instead of one full truncated cone, we are left with a truncated cone with a square hole passing through its middle.
Step 3: Compare options.
- (A): Shows cone split into small chunks, not correct.
- (B): Shows simple truncated cone (but cube effect missing). Wrong.
- (C): Shows cone with circular removal. Wrong (cube cuts square, not circle).
- (D): Shows truncated cone with four removed square-side cutouts – correct.
Final Answer: \[ \boxed{\text{D}} \]