Water is filled into a tank of base 40 cm x 40 cm. the water level rises 7.5 cm when 5 identical small marbles and 5 identical large marbles are into into the tanks and sick. If the volume of a large marble if two times that of the small one, what are the volumes of the marbles?
Vlm= 2Vsm
5Vsm + 5Vlm= 40x40x7.5 cm^2
substutited 10 Vsm for the 5Vlm, and solve.
To find the volumes of the marbles, let's start by setting up an equation.
Let Vsm be the volume of a small marble and Vlm be the volume of a large marble. We know that the volume of a large marble is twice the volume of a small marble, so we can write:
Vlm = 2Vsm
Next, we can use the information given about the water level rising when the marbles are added to set up another equation. The water level rises by 7.5 cm when 5 small marbles and 5 large marbles are added to the tank. The combined volume of the marbles is equal to the volume of water displaced, which is equal to the increase in water level multiplied by the base area of the tank:
5Vsm + 5Vlm = 40 cm * 40 cm * 7.5 cm^2
Now, we can substitute 2Vsm for Vlm in the equation and solve for Vsm:
5Vsm + 5(2Vsm) = 40 cm * 40 cm * 7.5 cm^2
5Vsm + 10Vsm = 40 cm * 40 cm * 7.5 cm^2
15Vsm = 40 cm * 40 cm * 7.5 cm^2
Vsm = (40 cm * 40 cm * 7.5 cm^2) / 15
Vsm = 3200 cm^3
Now, we can substitute this value back into the equation to find the volume of the large marble:
Vlm = 2Vsm
Vlm = 2 * 3200 cm^3
Vlm = 6400 cm^3
Therefore, the volume of the small marble is 3200 cm^3 and the volume of the large marble is 6400 cm^3.