Direction : Match the column I and II based on the given questions. If height…

Concept

To match Column I with Column II, find the unknown dimension (height of each solid) from its volume formula, then apply the rule that the cone's height must exceed the cylinder's height. Use π = 22/7.

Matching convention: in a "match the column" item like this, each Column-II entry is understood to back exactly one Column-I row (no value is reused across rows, and none is left unused) - this is the standard convention for this question format, and it is also the only reading under which the five answer choices are mutually exclusive, well-formed matches rather than overlapping partial descriptions.

Volume of a cone = (1/3)π r2 h, so h = 3V / (π r2).

Volume of a cylinder = π r2 h, so h = V / (π r2).

Also circumference = 2 π r, so a circumference of 44 m fixes r = 44 / (2 x 22/7) = 7 m - identical to option (B). A square inscribed in a circle is fixed by that circle's radius, so it is compatible with any given radius.

Application

Test each radius (A = 14 m, B = 7 m, C -> r = 7 m) against the two volumes:

Now assign radii so that height of cone > height of cylinder, each radius value serving one solid:

1. Cylinder (ii): take r = 14 m (A) -> height = 3 m.

2. Cone (i): with A used by the cylinder, the cone takes r = 7 m - stated as 7 m (B) or as circumference 44 m (C), since both give r = 7. Its height is 24 m.

3. Check the rule: 24 m (cone) > 3 m (cylinder) holds. So the cone matches either B or C and the cylinder matches only A.

4. Square (iii): a square inscribes in a circle of any radius, so it is consistent with r = 14 m (A) and with r = 7 m (B or C) - i.e. only A, either B or C.

Cross-check

If instead the cylinder took r = 7 m (h = 12 m) and the cone r = 14 m (h = 6 m), the cone height 6 m would be less than the cylinder height 12 m, violating the rule. So the cylinder must be the r = 14 m case and the cone the r = 7 m case - confirming (i) -> either B or C, (ii) -> only A, (iii) -> only A, either B or C.