Get comprehensive solutions to your questions with the help of IDNLearn.com's experts. Discover prompt and accurate answers from our community of experienced professionals.
Sagot :
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.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.