3 rectangular metal blocks,8 cm long, 6 cm wide & 5 cm high, were placed in an empty rectangular glass tank.water was then poured in until it reached a height of 10 cm. Another 5 similar blocks were put into the water so that it reached the brim of the tank. Assuming there was no loss in water, find a. The volume of water in the tank at first
B. The height of the tank
first step: figure the volume of the blocks.
To find the volume of water in the tank at first, we need to calculate the volume of the three rectangular blocks and the empty space above them.
The volume of each rectangular block can be found by multiplying its length, width, and height:
Volume of one block = 8 cm x 6 cm x 5 cm = 240 cm³
Since there are three blocks, the total volume of the three blocks is:
Total volume of the three blocks = Volume of one block x Number of blocks = 240 cm³ x 3 = 720 cm³
Next, we need to calculate the volume of the empty space above the blocks. The height of this empty space is given as 10 cm.
The volume of the empty space = length x width x height = 8 cm x 6 cm x 10 cm = 480 cm³
Now, to find the volume of water in the tank at first, we add the volume of the three blocks and the volume of the empty space:
Volume of water in the tank at first = Total volume of the blocks + Volume of empty space
= 720 cm³ + 480 cm³
= 1200 cm³
Therefore, the volume of water in the tank at first is 1200 cm³.
To find the height of the tank, we need to consider the fact that after adding 5 blocks to the tank, the water reaches the brim.
The volume of the additional 5 blocks is equal to the total volume of the water needed to fill the tank to the brim:
Volume of the additional 5 blocks = Volume of water to reach the brim
Since each block has a volume of 240 cm³, the volume of the additional 5 blocks is:
Volume of the additional 5 blocks = Volume of one block x Number of blocks = 240 cm³ x 5 = 1200 cm³
Therefore, the volume of the additional 5 blocks is 1200 cm³, which is equal to the volume needed to fill the tank to the brim.
Since the height of the tank is equal to the height of the water when it reaches the brim, we can conclude that the height of the tank is 10 cm.
Therefore, the height of the tank is 10 cm.