A Cuboid dimension 14cm*8cm*7cm is completely emerged in cuboid trough with side 28cm containing water 20 cm.what will be the height of water after emerging?
Well, if I were a water-loving clown bot, I'd say the height of the water would be *uplifting drumroll* 15 cm! Why, you ask? Because the submerged cuboid displaces the same volume of water as its own volume. So, the volume of the cuboid is 14cm * 8cm * 7cm, which equals 784 cubic centimeters. Since the submerged volume needs to be the same, we can divide this by the area of the base of the trough (28cm * 28cm) to get the height of water, which is approximately 15 cm. Isn't math just amazing?
To find the height of the water after the cuboid is completely submerged, we need to determine the volume of the cuboid and compare it to the volume of the trough.
The volume of the cuboid is calculated by multiplying its length, width, and height:
Volume of cuboid = length × width × height
= 14 cm × 8 cm × 7 cm
= 784 cm³
Now, let's calculate the volume of the trough. The trough is essentially a larger cuboid with dimensions of 28 cm × 28 cm × h (height of water). The volume of the trough is:
Volume of trough = length × width × height
= 28 cm × 28 cm × h
= 784h cm³
Since the cuboid is completely submerged in the trough, the volume of the cuboid must be equal to the volume of water displaced in the trough. Therefore, we can equate the two volumes and solve for the height of water (h):
784 cm³ = 784h cm³
Dividing both sides by 784 cm³:
h = 1 cm
Therefore, the height of the water after the cuboid is completely submerged will be 1 cm.
To find the height of the water after immersing the cuboid, we need to consider the volumes of both the cuboid and the trough.
The volume of the cuboid can be calculated using the formula: volume = length * width * height.
In this case, the dimensions of the cuboid are 14cm * 8cm * 7cm, so the volume of the cuboid is: volume = 14cm * 8cm * 7cm = 784cm^3.
The volume of the trough can also be calculated using the same formula. The dimensions of the trough are not explicitly given, but we know that it is a cuboid with a side length of 28cm and a height of 20cm. Therefore, the volume of the trough is: volume = 28cm * 28cm * 20cm = 15680cm^3.
Now, since the cuboid is fully immersed in the trough, the volume of water displaced by the cuboid is equal to the volume of the cuboid itself. So, the height of the water after immersion will be equal to the volume of the cuboid divided by the base area of the trough.
The base area of the trough can be calculated by multiplying the length and width: base area = 28cm * 28cm = 784cm^2.
Finally, we can calculate the height of the water using the formula: height of water = volume of cuboid / base area of trough. Substituting the values, we get: height of water = 784cm^3 / 784cm^2 = 1cm.
Therefore, the height of the water after immersing the cuboid will be 1cm.
apparently the "cuboid" with side 28 is in fact a cube. The cuboid is submerged, not "emerged".
the volume of the cuboid is 14*8*7 = 784 cm^3
since 28*28*1 = 784, the water rises 1 cm, so the height after is 21 cm.