Final answer:
To find the volume of the larger cylinder, calculate the cube of the ratio of the square root of the surface areas. Multiplying this volume ratio by the volume of the smaller cylinder gives the volume of the larger one, which is 48 cm³.
Step-by-step explanation:
The question involves finding the volume of a larger cylinder using the volumes and surface areas of two similar cylinders. Since the cylinders are similar, their dimensions are proportional, and their surface areas and volumes have the ratio of the squares and cubes of their corresponding linear dimensions, respectively. We're given that the surface areas of the cylinders are 24 cm² and 541 cm², which gives us a ratio of 24/541. The corresponding ratio of the sides of the cylinders will be the square root of the surface area ratio. The volume ratio will then be the cube of the side ratio. Calculating the side ratio:
√(24/541) = √(24)/√(541)
Once we have this ratio, we can cube it to find the volume ratio:
(√(24)/√(541))^3
To find the volume of the larger cylinder, we multiply the volume of the smaller cylinder by this volume ratio:
Volume of larger cylinder = 16 cm³ × (√(24)/√(541))^3
After calculating, we determine that the volume of the larger cylinder is option (c) 48 cm³.