A cube with edge length x and a right cylinder with circular base have the same volume. Find x ,in cm, if the radius of the cylinder is 5 cm and its height is 5 cm.

Question

anonymous · Answer

please help

anonymous · Answer

Setup of the problem is important. The volume of the cube is $$x^{3}$$
We set that equal to the volume of the cylinder. The volume of a right cylinder is:
$$base area * height$$
So we have:
$$x ^{3} = \pi(5^{2}cm)(5cm)$$
$$x ^{3}= \pi125cm ^{3}$$
Take the 1/3 power on both sides and you get:
$$x = 5\sqrt[3]{\pi}cm$$

anonymous · Answer

it is the same 5 (pi)1/3?

anonymous · Answer

Yes

anonymous · Answer

ok I understand now. Thanks for your help.

anonymous · Answer

The 3 in front is a fractional power. Just as square root would be x^(1/2)