Solution check for a Rate problem

[opus]

Homework Statement

A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled with identical pieces of candy, each with a volume of 50.0$mm^3$ and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kilograms per minute) does the mass of the candies in the container increase?

Homework Equations

The Attempt at a Solution

Please see attached image to see my work and drawings. My solution is boxed in the bottom, but the text doesn't have a solution to this problem so I'm unsure if it's correct or not.

 

[Andrew Mason]

Homework Statement

A vertical container with base area measuring 14.0 cm by 17.0 cm is being filled witqh identical pieces of candy, each with a volume of 50.0$mm^3$ and a mass of 0.0200 g. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of 0.250 cm/s, at what rate (kilograms per minute) does the mass of the candies in the container increase?

Why does $\pi$ appear in your solution?

AM

 

[Delta2]

I didn't check the arithmetic operations but your method looks correct to me. We are not given whether each candy is spherical, but we are given that the space between the candies is negligible and I think that's enough.

 

[opus]

Why does $\pi$ appear in your solution?

AM

That was unnecessary information that I came up with, but the reason it's there is because I used the volume of a sphere formula to get the radius and the diameter of each candy but I ended up not needing those.

 

[opus]

I didn't check the arithmetic operations but your method looks correct to me. We are not given whether each candy is spherical, but we are given that the space between the candies is negligible and I think that's enough.

Ok that's all I needed to know- if the method was correct or not. I was initially under the impression that I'd need to find the diameter of each candy to see how many I could fit in the base laying flat but that seemed not needed. Thank you.