The ratio of the red-eye of two similar cylinders is 3:5. The volume of the smaller cylinder is 54π cubic centimeters. Find the volume of larger cylinder.

Question

The options are:

(A) 90π cm^3

(B) 150π cm^3

(C) 250π cm^3

(D)40 cm^3

Answer 1

OK, it took me several minutes to figure out that "red-eye" is actually radii (the plural of radius). Since the two cylinders are similar, the scale factor from the smaller to the larger cylinder is 5/3. The ratio of their surface areas is thus (5/3)² and the ratio of the volumes is (5/3)³:

Volume of Bigger Cylinder = (5/3)³ × Volume of Smaller Cylinder

Volume of Bigger Cylinder = (125/27) × 54π = ____?

Leave the answer in terms of π.