Answer:
9 times larger and 9 times smaller (it changes by the square of the change factor of the radius).
Step-by-step explanation:
the reason :
the formula of the volume of a cone is base area times height divided by 3.
and the base area is the area of a circle with radius r.
=> Vc = pi×r²×height / 3
now, when we multiply r by a factor, like in our examples here by 3 and also by 1/3, then this factor also gets squared in the calculation of that formula.
so, if the new radius is 3×r, then the formula looks like
Vc = pi×(3r)²×height / 3 = pi×9r²×height / 3
so, as you can see, when we triple the radius, we introduce the factor 9 (square of 3) into the volume, and therefore the volume increases by the factor 9.
similar, when we divide the radius by 3
Vc = pi×(r/3)²×height / 3 = pi×(r²/9)×height / 3
we introduce the factor 1/9 into the volume, and it decreases to 1/9th of its original size.
