Two beach balls are each in the shape of a sphere. The larger beach ball has a diameter of 3x, and the smaller beach ball has a diameter of x. What is the ratio of the volume of the larger beach ball to volume of the smaller beach ball?

The correct answer is: 27 to 1

HINT: Use the formula of volume of sphere and find the ratios.
Complete step by step Solution
We know that, the Volume of a sphere:
Diameter of larger beach ball = 3x
Volume of larger beach ball with radius = =
[Diameter is 3x, hence radius is ]
Diameter of smaller beach ball = x
Volume of smaller beach ball with radius
[Diameter is x, hence radius is ]
Ratio =
Hence, we can conclude that the volume of the larger sphere to be 27 times that of the smaller sphere.
Option D is the correct answer.

volume of a sphere
A sphere is a collection of points in space separated by r from the center. The quantity of space a solid in three dimensions takes up is known as its volume. The unit of volume is measured in cubic (in³, ft³, cm³, m³, et cetera). Before calculating the volume, ensure all measurements are in the same unit.
Follow the steps below to determine the volume of a given sphere:
Step 1: Compare the radius of the given sphere. If you know the diameter of the sphere, divide it by two to get the radius.
Step 2: Find the radius of r'³s cube.
Step 3: Now divide it by (4/3) π
Step 4: The volume of the sphere will be the final answer.
The volume V of a sphere is equal to four-thirds of pi times the cube of the radius.
V = 4/3πr³
A hemisphere's volume is equal to one-half that of its related sphere.