Franco wants to double the volume of the cone. What should he do?

Question

asked Oct 15, 2020 3.4k views

2 Answers

Ashtav · Answer 1 · 2020-10-18T18:03:14+0000

Answer:

If Franco wants to double the volume, he must multiply the radius and height of the original cone by
$\sqrt[3]{2}$

Explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> the volume of the larger cone

y----> the volume of the original cone

so

z^(3)=(x)/(y)

we have

$x=2V\ units^(3)$

$y=V\ units^(3)$

substitute and solve for the scale factor

z^(3)=(2V)/(V)=2

$z=\sqrt[3]{2}$ ------> the scale factor

If Franco wants to double the volume, he must multiply the radius and height of the original cone by
$\sqrt[3]{2}$