Respuesta :

CastleRook
Given that the height is reduced by 2/5 and the radius is doubled, the new volume will be given by:
V=1/3πr^2h
r=2r
h=2/5h
thus;
V=1/3*π*(2r)^2(2/5h)
=8/15πr^2h
This implies that the new volume will be 8/15 of the original volume

Answer:

Option (D) is correct.

Step-by-step explanation:

Let the initial original height of the cone is h and radius is r.

The volume of original cone is given by

[tex]V=\frac{1}{3}\times \pi r^{2}\times h[/tex]

Now the new height be h' = 2/5 h and radius r' = 2r

So, the new volume be

[tex]V'=\frac{1}{3}\times \pi r'^{2}\times h'[/tex]

[tex]V'=\frac{1}{3}\times \pi\times  2r^{2}\times \frac{2}{5}h[/tex]

[tex]V=\frac{8}{15}\times \pi \times r^{2}h[/tex]

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