hugo has a cylindrical container that holds marbles. the container has a height of 10 inches and radius of 5 inches. each marble is shaped like a sphere with a radius of 1 inch. if there are 150 marbles in the container, how much empty space is in the container

157.1 in³

Step-by-step explanation:

In order to solve this question, we need to know the volume of that cylindrical container and the volume of the sphere (this is to know the capacity of the cylinder ie how much it can take and the amount of space the sphere can occupy).

Volume of a cylinder is=

pi * r² * h

Volume of a sphere is

4/3 * pi * r²

And here we were given the radius of the cylindrical container as 5 inches and its height as 10 inches

The radius of the sphere is 1 inch.

Applying this in the formula we have,

For cylinder:

22/7 * 5² * 10 = 785.7 in³

For the sphere:

4 : 3 * 22/7 * 1² = 4.19 in³

And if there are 150 marbles in the container, it is going to occupy a total space of 628.57 in³.

Therefore, the remaining space left in the cylinder will be 785.7 - 628.57 = 157.1 in³