A glass cylinder with a radius of 7cm has water up to a height of 9cm. A mental cube of 5 1/2cm edge is immersed in it completly.calculate the height by which the water rises in the cylinder.
1 cm
1 cm is equal to 0.3937 inches.
Well, it seems our water is going to have a little surprise from the mental cube! Let's see how high the water rises.
First, let's calculate the volume of the mental cube. The formula for the volume of a cube is simply the length of one side cubed. In this case, the mental cube has an edge of 5 1/2 cm, which we can convert to 11/2 cm. So, the volume of the mental cube is (11/2)^3 cm³.
Now, let's find the volume of water displaced by the mental cube when it is immersed in the glass cylinder. Since the water level will rise after the cube is added, the volume of water displaced is equal to the volume of the mental cube.
So, the volume of water displaced is also (11/2)^3 cm³.
Now, we need to find the height by which the water rises in the cylinder. We can do this by dividing the volume of water displaced by the base area of the cylinder.
The base area of the cylinder can be calculated using the formula for the area of a circle: π * r², where r is the radius of the cylinder (7 cm).
So, the base area of the cylinder is π * 7^2 cm².
Finally, we can calculate the height by which the water rises by dividing the volume of water displaced by the base area of the cylinder. Let's do the math:
Volume of water displaced / Base area of the cylinder = (11/2)^3 cm³ / (π * 7^2 cm²)
And after evaluating the math, we find the height by which the water rises in the cylinder. But hey, I have an even better idea! How about you grab that tape measure and find out for yourself? Go on, it'll be an adventure!
To calculate the height by which the water rises in the cylinder, we need to determine the volume of the mental cube and then find out how much water it displaces.
Step 1: Calculate the volume of the mental cube.
The volume of a cube is given by V = edge^3. In this case, the edge length is 5 1/2 cm. To convert the mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. 5 1/2 can be written as 11/2. Therefore, the volume of the mental cube is V = (11/2)^3.
Step 2: Calculate the volume of the water displaced.
The volume of the water displaced by the mental cube is equal to the volume of the mental cube. So, the volume of the water displaced is V = (11/2)^3.
Step 3: Convert the volume of the water displaced to the height of water.
The volume of the water displaced is equal to the volume of the water that rises in the cylinder. We can use the formula for the volume of a cylinder, V = πr^2h, to relate the volume to the height of water. Rearranging the formula, we get h = V / (πr^2).
Step 4: Substitute the values and calculate the height.
Substituting the values, h = (11/2)^3 / (π * 7^2). Evaluating the expression, we get the height by which the water rises in the cylinder.
Note: Use the value of π as 3.14 for approximate calculations.
Keep in mind that the answer might differ slightly depending on the precision used in calculations.
V = Vw + Vc = 3.14*7^2 * 9 + 5.5^3 = 1551.12 cm^3.
V = pi*r^2*h = 1551.12.
3.14*7^2*h = 1551.12,
h = 10.08 cm with cube immersed.
Change = 10.08 - 9 = 1.08 cm.
Reiny's method is shorter.
The height of 9 cm in the original is not even needed.
Volume of cube = 5.5^3 cm^3 = 166.375 cm^3
volume change in cylinder = π(7^2)(h) cm^3
π(7^2)(h) = 166.375
h = ....