Question

A cylindrical bucket and spherical storage container are shown. The bucket has a radius of 6 inches and a height of 15 inches, and the storage container has a diameter of 24 inches. Nicholas says he can fill the entire storage container with seef by filling the bucket four times and pouring the contents into the container. Is Nicholas correct? Explain why or why not.

Answer 1

since the ratio of both volumes is approximately 4, then we can say Nicholas is correct

Explanation:

Firstly, what we need to do is to calculate the volume of both.

For the cylindrical bucket, the volume can be calculated as

pi * r^2 * h

where r is 6 inches and h is 15 inches

The volume is thus

pi * 6^2 * 15 = 540pi inches*3

For the spherical storage, the volume can be calculated using the formula

V = 4/3 * pi * r^3

with r = d/2 = 24/2 = 12 inches

The volume is thus;

V = 4/3 * pi * 12^3 = 2,304 pi inches^3

Now, to confirm the validity of Nicholas’ claims, we shall divide the volume of the spherical storage by the volume of the cylindrical container.

Mathematically that would be 2,304pi/540 pi = 4.267 which is approximately 4 times