George and phil were playing with their fish tank again. they had a difficult time keeping their fish tank is 100 cm long, 60 cm wide and 40 cm high. they tilted the tank resting on a 60 cm edge, with the water level reaching the midpoint of the base. when they rest the tank down to a horizontal position, what is the depth of the water in cm?
Draw a side view of the tank, and assume they tilted it until the water reached the mid-point of the base because it started spilling over the top edge. A drawing will show a triangle with a base of 50 cm and a height of 40 cm in that position. The area formula (you should know) gives 1000 cm2 x 60 cm for 60,000 cm3 of water.
Since the base area is 6,000 cm2, the water will be 10 cm high (vol/area base).
Tough on fish though....
To find the depth of the water when the tank is in a horizontal position, we first need to understand the dimensions of the tank and the water level.
The dimensions of the tank are:
- Length: 100 cm
- Width: 60 cm
- Height: 40 cm
When the tank is tilted on a 60 cm edge and the water level reaches the midpoint of the base, we can visualize this as a triangle with a base of 50 cm (half of the length) and a height of 40 cm (the height of the tank).
Using the formula for the area of a triangle (1/2 * base * height), we can calculate the area of this triangle. In this case, it will be 1/2 * 50 cm * 40 cm = 1000 cm^2.
Since we know the volume of water in the tank is 60,000 cm^3 (calculated by multiplying the base area by the width of the tank), we can divide this volume by the base area to find the height or depth of the water.
60,000 cm^3 / 1000 cm^2 = 60 cm
Therefore, when the tank is in a horizontal position, the depth of the water will be 60 cm.
It's worth noting that a water level of 60 cm might be tough on the fish inhabiting the tank, as it leaves very little space for them. They might need a deeper tank to allow for better swimming and living conditions.