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.
The 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
Avg volume = (4/3)π(1.69)^3
= appr 20.22 cm^3
check my arithmetic
To find the average volume of the 12 marbles, we first need to find the change in volume of the water when the marbles were added.
The initial volume of the water in the tank can be calculated by multiplying the length, width, and depth:
Initial volume = length * width * depth = 28 cm * 18 cm * 7 cm
After adding the 12 marbles, the volume of water in the tank increased, which can be calculated by multiplying the increase in depth by the area of the base of the tank:
Increase in volume = increase in depth * area of base = (12 cm - 7 cm) * (28 cm * 18 cm)
To find the volume of each marble, we need to divide the increase in volume by the number of marbles:
Average volume of each marble = increase in volume / number of marbles = [(12 cm - 7 cm) * (28 cm * 18 cm)] / 12
So, to find the average volume of the 12 marbles, divide the increase in volume by 12:
Average volume of each marble = [(12 cm - 7 cm) * (28 cm * 18 cm)] / 12
Now, calculate the expression to find the average volume of each marble.