All of the water from a full cylindrical tank is drained into a rectangular aquarium. The cylinder has a height of 50cm and a diameter of 30cm. How deep is the water in the aquarium, if it has a rectangular base measuring 40cm by 20cm.
volume of tank is v = π(15^2)(50)
depth of water is d = v/(20*40)
To find the depth of the water in the rectangular aquarium, we need to determine the volume of water that has been drained from the cylindrical tank and then divide that volume by the base area of the rectangular aquarium.
Step 1: Calculate the volume of the cylindrical tank.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the cylinder is 30 cm, the radius (r) is half of the diameter, which is 30/2 = 15 cm.
Substituting the values into the formula, we get V = π(15)^2(50) = 11,250π cm^3.
Step 2: Calculate the depth of the water in the rectangular aquarium.
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
Given that the base of the rectangular aquarium has dimensions 40 cm by 20 cm, the base area (A) is l × w = 40 × 20 = 800 cm^2.
If the entire volume of the cylindrical tank is poured into the rectangular aquarium, the depth (d) can be calculated as d = V / A.
Substituting the values, we get d = (11,250π) / 800 ≈ 14.06 cm.
Therefore, the water in the rectangular aquarium would be approximately 14.06 cm deep.
To find the depth of the water in the aquarium, we need to determine the volume of water drained from the cylindrical tank and then divide it by the base area of the aquarium.
1. First, let's find the volume of the cylindrical tank. The formula to calculate the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cylinder is 30 cm, the radius (r) is half of the diameter, which is 15 cm (or 0.15 m).
The height (h) of the cylinder is 50 cm (or 0.5 m).
Plugging these values into the formula, we get:
V_cylinder = π * 0.15^2 * 0.5
2. Now, let's calculate the volume of the rectangular aquarium. The formula to calculate the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
Given that the length (l) is 40 cm (or 0.4 m), the width (w) is 20 cm (or 0.2 m), and we need to find the height (h).
Rearranging the formula, we have:
h = V_aquarium / (lw)
Since the volume of the aquarium is unknown, we need to find it first.
3. Calculate the Volume of the Water Drained:
Subtracting the volume of the rectangular aquarium from the volume of the cylindrical tank will give us the volume of water drained:
V_water_drained = V_cylinder - V_aquarium
4. Now, we can calculate the height of the water in the aquarium:
h = V_water_drained / (lw)
Plugging in the values, we get:
h = (V_cylinder - V_aquarium) / (lw)
Substitute the values from steps 1 and 2, and simplify the equation to find the height (h) of the water in the aquarium.