a) The ratio of the lengths of the sides of two squares is 1:4. What is the ratio of the are of the two squares?
b) The ratio of the lengths of the sides of two cubes is 2:5. What is the ratio of the volumes?
I don't get these questions :/
If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
If two polygons are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
a) ( 1 / 4 ) ^ 2 = 1 / 16
b ) ( 2 / 5 ) ^ 2 = 8 / 125
b ) ( 2 / 5 ) ^ 3 = 8 / 125
Thanks :)
No worries, I'm here to help! Let's break down each question step by step.
a) The ratio of the lengths of the sides of two squares is 1:4. To find the ratio of the areas, we need to compare the areas of the two squares.
To calculate the area of a square, you need to multiply the length of one side by itself. So, if the length of one side of the first square is 'x', then the length of the second square will be '4x' because the sides are in a ratio of 1:4.
Now, let's calculate the areas. The area of the first square will be x * x = x^2, and the area of the second square will be (4x) * (4x) = 16x^2.
Therefore, the ratio of the areas of the two squares is x^2 : 16x^2. However, we can simplify this ratio further by dividing both terms by x^2. This gives us a simplified ratio of 1:16. So, the ratio of the areas of the two squares is 1:16.
b) The ratio of the lengths of the sides of two cubes is 2:5. To find the ratio of the volumes, we need to compare the volumes of the two cubes.
The volume of a cube is calculated by multiplying the length of one side by itself twice. So, if the length of one side of the first cube is 'x', then the length of the second cube will be '5x' because the sides are in a ratio of 2:5.
Now, let's calculate the volumes. The volume of the first cube will be x * x * x = x^3, and the volume of the second cube will be (5x) * (5x) * (5x) = 125x^3.
Therefore, the ratio of the volumes of the two cubes is x^3 : 125x^3. We can simplify this ratio by dividing both terms by x^3. This gives us a simplified ratio of 1:125. So, the ratio of the volumes of the two cubes is 1:125.
Remember, in this type of problem, we need to square the side lengths for squares and cube the side lengths for cubes to find the areas and volumes, respectively.