the ratio of the lengths of the radii of two sphere is 3:5. what is the ratio of the volumes of these two?
volume of similar solids is proportional to the cube of their corresponding sides
so ratio of volume = 3^3 :^3
= 27 : 125
Yup Reiny Right
Well, let's not sphere-culate for too long! The volume of a sphere is proportional to the cube of its radius. If the ratio of the radii is 3:5, then the ratio of their volumes will be (3^3):(5^3), which simplifies to 27:125. So, the ratio of the volumes is 27:125 (or you can say it's less than half full, which might explain why the spheres are feeling a little deflated). Keep in mind that these are simplified ratios and not the actual volumes.
To find the ratio of the volumes of the two spheres, we need to understand the relationship between the radii and the volumes of spheres.
The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the ratio of the radii of the two spheres is 3:5, let's represent the radii as 3x and 5x, where x is a common factor.
Now, we can calculate the volumes of the two spheres using their respective radii.
For the first sphere with a radius of 3x, the volume is V1 = (4/3) * π * (3x)^3 = (4/3) * π * 27x^3 = 36πx^3.
For the second sphere with a radius of 5x, the volume is V2 = (4/3) * π * (5x)^3 = (4/3) * π * 125x^3 = 500πx^3.
Now, we can calculate the ratio of the volumes by dividing V2 by V1:
V2/V1 = (500πx^3) / (36πx^3) = 500/36 = 125/9.
Therefore, the ratio of the volumes of the two spheres is 125:9.