Let's pick some simple points with which to set up an example for ourselves for this. Let's let the smaller radius be 1, and the larger, twice that, be 2. The radius itself is a single unit measure; in other words, it's measured as inches, feet, cm, etc., while the volume is a cubed measure. Volume is measured in inches cubed, feet cubed, cm cubed, etc. Therefore, if we have the radii measuring 1:2, we simply cube those single unit measures to find the ratio of their volumes. 1 cubed is 1, and 2 cubed is 8. So your answer for this is 1/8.
The ratio of the volumes of the two spheres when the radius of one sphere is twice as great as the radius of the second sphere is 1/8. Hence, 3rd option is the right choice.
The volume of any body is the total space it occupies.
The volume of a sphere is calculated using the formula:
V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
In the question, we are asked to find the ratio of the volumes of the two spheres when the radius of one sphere is twice as great as the radius of the second sphere.
Assuming the radius of the first sphere to be r, we get the radius of the second sphere to be 2r.
The volume of the first sphere is, V₁ = (4/3)πr³.
The volume of the second sphere is, V₂ = (4/3)π(2r)³ = (4/3)π(8r³).
Thus, the ratio of their volumes can be shown as:
V₁/V₂ = {(4/3)πr³}/{(4/3)π(8r³)} = 1/8.
Thus, the ratio of the volumes of the two spheres when the radius of one sphere is twice as great as the radius of the second sphere is 1/8. Hence, 3rd option is the right choice.
Learn more about the volume of a sphere at
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