a rectangular tank 28cm long and 18cm wide was filled with water to a dept of 7cm. When 12 marbles were added the level rose to 12cm. Find the average volume of the 12 marbles.

Change in volume

= (28)(18)(5) cm^3
= 2520 cm^3
This was caused by the 12 marbles
that volume was 12(4/3)πr^3
= 16πr^3

16πr^3 = 2520
r^3 = 2520/(16π)
r = (2520/(16π))^(1/3)
I got appr 1.69 cm

check my arithmetic

so you are saying the average volume for 1 marble is appr. 1.69cm?

no, I found the average radius r

I was hoping you would be able to find its volume.
V = (4/3)π r^3 , (I used it)

OHHHH I'm so sorry, havent done this in years, now i understand thank you so very very much!!!

To find the average volume of the 12 marbles, we first need to determine the change in volume of the tank after adding the marbles.

We are given that the tank is initially filled with water to a depth of 7cm. When 12 marbles are added, the level rises to 12cm. This means that the 12 marbles displaced 5cm of water.

The volume of water displaced by the 12 marbles is equal to the volume of the 5cm of water they displaced from the tank. To find this volume, we need to calculate the volume of the rectangular tank.

The formula for the volume of a rectangular tank is V = length x width x height. In this case, the length is 28cm, the width is 18cm, and the height is 5cm.

V = 28cm x 18cm x 5cm = 2520 cm³

Therefore, the 12 marbles displaced 2520 cm³ of water.

Since we want to find the average volume of the 12 marbles, we divide the total volume of the marbles by the number of marbles (12).

Average volume of the 12 marbles = 2520 cm³ / 12 = 210 cm³.

Hence, the average volume of the 12 marbles is 210 cm³.