Kevin has a salt water aquarium.As
Shown below in the shape of a rectangular prism. ( base 36 in, width 18in,height 20 in) . When a rock is submerged into the aquarium the water level rises 0.25 inches. What is the voulume of the rock ?
as a block of water, the displaced fluid is
36*18*0.25 = 162 in^3
To find the volume of the rock, we need to determine the change in volume of the water when the rock is submerged.
The volume of the water in the aquarium is given by the formula:
Volume = Base Area x Height
=> Volume = 36 in x 18 in x 20 in
=> Volume = 12,960 in³
When the rock is submerged, the water level rises by 0.25 inches. We can calculate the change in volume by multiplying the cross-sectional area of the aquarium by the change in height:
Change in Volume = Base Area x Change in Height
=> Change in Volume = 36 in x 18 in x 0.25 in
=> Change in Volume = 1,620 in³
Therefore, the volume of the rock can be calculated by subtracting the change in volume from the initial volume of the water:
Volume of the Rock = Volume of Water - Change in Volume
=> Volume of the Rock = 12,960 in³ - 1,620 in³
=> Volume of the Rock = 11,340 in³
So, the volume of the rock is 11,340 cubic inches.
To find the volume of the rock, we need to determine the volume of water displaced when the rock is submerged in the aquarium.
The volume of the rock can be calculated by the equation:
Volume of rock = Volume of water displaced
The volume of the water displaced is equal to the increase in the volume of the aquarium:
Volume of water displaced = Change in height * base area of the aquarium
Given:
Base length = 36 inches
Width = 18 inches
Height = 20 inches
Change in height = 0.25 inches
First, we need to calculate the base area of the aquarium:
Base area of the aquarium = Base length * Width
Base area of the aquarium = 36 inches * 18 inches
Base area of the aquarium = 648 square inches
Next, calculate the volume of water displaced:
Volume of water displaced = Change in height * base area of the aquarium
Volume of water displaced = 0.25 inches * 648 square inches
Volume of water displaced = 162 cubic inches
Finally, the volume of the rock is equal to the volume of water displaced:
Volume of rock = 162 cubic inches
Therefore, the volume of the rock is 162 cubic inches.