Question

If a cone has a height of 5 cm and a volume of 128π cm³

find the diameter of the circular base.

Answer 1

Using the formula of a volume of the cone we can find its area:

`V=(1)/(3)A*h`

`A=(3V)/(h)`

Using the formula of an area of the circle we can now find the radius of cone's base:


`A=\pi r^2`

`(3V)/(h)=\pi r^2`

`r^2=(3V)/(h \pi)`

`r=\sqrt{(3V)/(h \pi)`

The diameter of circle is twice of its radius, so:

`d=2\sqrt{(3V)/(h \pi)`

`d=2\sqrt{(3*128\pi)/(5\pi)}=2\sqrt{(384)/(5)}\approx17.53`

So, the diameter of cone is approximately equal to 17.53cm.

Answer 2

The volume of a cone with respect to its diameter is:

V=(hπd^2)/12 solving this for d we have:

d=√[(12V)/(hπ)], we are given that V=128π and h=5 so

d=√(1536π)/(5π)

d=√(1536/5)

d=√307.2 cm

d≈17.53 cm (to nearest hundredth)