TWO EGGS ARE SIMILAR IN SHAPE WITH MASS 50 G AND 70G THE HEIGHT OF BIGGER EGG IS 8 CM FIND THE HEIGHT OF SMALLER EGG
SCALE FACTOR K=0.238
To find the height of the smaller egg, we can use the scale factor and the given information about the mass of the eggs.
First, we need to determine the relationship between the mass and the volume of an egg. We can assume that the density of both eggs is the same. Density is defined as mass divided by volume.
Density = Mass / Volume
Since the density of both eggs is the same, we can set up the following equation:
Density of Bigger Egg = Density of Smaller Egg
Mass of Bigger Egg / Volume of Bigger Egg = Mass of Smaller Egg / Volume of Smaller Egg
We are given the mass of the bigger egg (70 g), so let's label it as M1, and the mass of the smaller egg (50 g) as M2. The volume of the bigger egg will be V1, and the volume of the smaller egg will be V2.
Therefore, we have the following equation:
M1 / V1 = M2 / V2
Next, we can use the scale factor (k) to relate the volumes of the two eggs. The scale factor relates the measurements of two similar objects. In this case, the height of the bigger egg is 8 cm, so we can use it to find the height of the smaller egg.
k = Height of Smaller Egg / Height of Bigger Egg
With k = 0.238 and the height of the bigger egg as 8 cm, we can substitute these values into the equation:
0.238 = Height of Smaller Egg / 8 cm
Now, we can rearrange the equation to solve for the height of the smaller egg:
Height of Smaller Egg = 0.238 * 8 cm
Height of Smaller Egg = 1.9 cm
Therefore, the height of the smaller egg is 1.9 cm.