A rectangular tank,15cm and 20cm wide, was filled with water to a depth of 6cm. When a stone of volume 1800 cm³ was put in the water, the water level rose to 3/4 of the height of the tank. Find the height of the tank.
Height of the tank = (1800 cm³ + (15 cm x 20 cm x 6 cm)) / (15 cm x 20 cm)
= (1800 cm³ + 1200 cm³) / 300 cm²
= 3000 cm³ / 300 cm²
= 10 cm
To solve this problem, we can use the concept of volume.
Let's start by finding the initial volume of water in the tank before the stone was added. The tank is rectangular, so we have:
Volume of water in the tank = length * width * height
Given that the width is 20 cm and the depth of the water is 6 cm, we need to find the length of the tank.
The water level rises to 3/4 of the height of the tank when the stone is added. This means that the height of the water after adding the stone is (3/4) * height of the tank.
Now, let's calculate the volume of the stone. We are given that the volume of the stone is 1800 cm³.
The total volume of the tank after adding the stone is the sum of the volume of water and the volume of the stone.
Using the given information, we can set up the equation:
(length) * (20) * ((3/4) * height of the tank) = (length) * (20) * 6 + 1800
Simplifying the equation, we have:
15 * 20 * ((3/4) * height of the tank) = 15 * 20 * 6 + 1800
Next, we can cancel out the common factors and solve for the height of the tank:
(3/4) * height of the tank = 6 + 1800 /(15 * 20)
Simplifying the right side of the equation:
6 + 1800 /(15 * 20) = 6 + 1800 /300 = 6+6 = 12
Now, we have:
(3/4) * height of the tank = 12
To find the height of the tank, we can multiply both sides of the equation by (4/3):
height of the tank = 12 * (4/3)
Simplifying further:
height of the tank = 16 cm
Therefore, the height of the tank is 16 cm.
To find the height of the tank, we need to use the information given and solve step by step.
Let's start by calculating the initial volume of water in the tank before placing the stone.
The initial volume of water = length × width × depth
= 15 cm × 20 cm × 6 cm
= 1800 cm³
Since the stone has a volume of 1800 cm³, it displaces an equal volume of water when placed in the tank. This means the water level will rise by 1800 cm³.
Now, let's find the new height of the water after placing the stone.
The new volume of water = Initial volume of water + Volume displaced by the stone
= 1800 cm³ + 1800 cm³
= 3600 cm³
The new height of the water = Volume of water / (length × width)
= 3600 cm³ / (15 cm × 20 cm)
= 12 cm
But the question states that the new water level is 3/4 of the height of the tank. So, let's find the height of the tank.
Height of the tank = (New height of water) / (3/4)
= 12 cm / (3/4)
= 16 cm
Therefore, the height of the tank is 16 cm.