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 by filling the bucket 4 times and pouring the contents into the container. Is Nicholas correct? Why or why not.

Answer 1

Answer:

To know if Nicholas is correct

4(540π) inches³ ≥ 2304π inches³

Unfortunately, 2160π inches³ is less than 2304π inches³. This means Nicholas is absolutely wrong .4 times the volume of the cylindrical bucket is less than the volume of the spherical tank.  

Step-by-step explanation:

The question wants you to look for the volume of the cylindrical bucket and the spherical bucket and know if 4 times the volume of the cylindrical bucket will fill the spherical tank.

volume of a cylinder = πr²h

where

r = 6 inches

h = 15 inches

volume of the cylinder bucket = πr²h

volume of the cylinder bucket= π × 6² × 15

volume of the cylinder bucket = π × 36 × 15

volume of the cylinder bucket = 540π inches³

volume of the spherical storage container

volume = 4/3πr³

r = 24/2 = 12 inches

volume = 4/3 × π × 12³

volume = 4/3 × π × 1728

volume = 6912π/3

volume = 2304π inches³

To know if Nicholas is correct 4(540π) inches³ ≥ 2304π inches³

Unfortunately, 2160π inches³ is less than 2304π inches³. This means Nicholas is absolutely wrong .4 times the volume of the cylindrical bucket is less than the volume of the spherical tank.