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Explanation:

Let V1 be the original volume and r1 and h1 be the radius and height of the cone respectively.

V113 × π × (r1)2 × h1. Consider statement I. If the cone is cut parallel to base and dividing the height in
the ratio 1 : 2, then r212×r1 and h212 × h1, where r2 and h2 are the radius and height of the new
cone respectively. If V2 is the volume of new cone, then V2 = 13 × π(r2)2 × h2

=13×π×12×r12×12h1=18×V1

Hence, statement I alone is sufficient to answer the question (as we get the ratio as 1 : 8).

Similarly, based on statement II alone, we can find the ratio (which will be 1 : 27).

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