A glass cylinder with a radius 7 cm has water up to a height of 9 cm. A metal cube of 5 1/2 cm edge is immersed in ti completely. Calculate the height by which the water rises in the cylinder.
volume of cube = (5.5 cm)^3 = 166.375 cm^3
then our cylinder's height would increase by h , such that
π(49)h = 166.375
h = 1.081 cm
(note that the 9 cm depth of water did not enter the picture)
Give
h=1 m
r=0.7 m
solution
A=2*3.14*r(h+r) =6.28*0.7m(1m+0.7m)
=7.47 m^2
where A- total surface area
V=3.14*r^2h
=3.14*0.7*0.7*1
=1.54 m^3
where V- volume
Yes, you are correct! Since the height of the water needed is very small compared to the height of the cylinder (9 cm), we can approximate the solution by taking h to be 1 cm.
volume of cube = (5.5 cm)^3 = 166.375 cm^3
then our cylinder's height would increase by h , such that
π(49)h = 166.375
h = 1.081 cm
So,h~1(h is approximately 1)
To calculate the height by which the water rises in the cylinder when a metal cube is immersed in it, we need to consider the volume of the cube and the volume of water displaced by it.
First, let's find the volume of the cube. The formula to calculate the volume of a cube is V = s^3, where V is the volume and s is the length of the side.
Given that the edge of the cube is 5 1/2 cm, we need to convert it to an improper fraction:
5 1/2 = (2*5 + 1)/2 = 11/2
Now we can calculate the volume of the cube:
V_cube = (11/2)^3
Next, let's find the volume of water displaced. When a solid object is immersed in a liquid, it displaces the same volume of liquid as its own volume. So, the volume of water displaced will be equal to the volume of the cube.
V_displaced = V_cube = (11/2)^3
Since the volume of water displaced is equal to the volume of the cube, and the volume of the cylinder is equal to the product of its base area and height, we can find the height by rearranging the formula.
The area of the cylinder's base can be calculated using the formula A = π*r^2, where A is the area and r is the radius.
Given that the radius of the cylinder is 7 cm, we can calculate the base area:
A_base = π * 7^2
Now, we can find the height of the water displaced:
h_displaced = V_displaced / A_base
Substituting the values, we get:
h_displaced = (11/2)^3 / (π * 7^2)
Evaluating this expression will give us the height by which the water rises in the cylinder when the cube is completely immersed.