Respuesta :

penfila11Pen
Lets get started :)

We need to find the radius of the larger cylinder

V = [tex] \pi [/tex]r²h
960 = [tex] \pi [/tex]r²(16)
[tex] \frac{960}{16} = \pi r^2[/tex]
60 = [tex] \pi r^2[/tex]
[tex] \frac{60}{ \pi } = r^2 [/tex]
r = [tex] \sqrt{ \frac{60}{ \pi } } [/tex]
r ≈ 4.27 cm

The ratio of the bigger cylinder to smaller is:
16 : 4

Therefore, the big cylinder is 4 times bigger than the small cylinder

[tex] \frac{4.37}{4} [/tex] = r
r = 1.09 cm (radius of small cyclinder)

V (small cylinder) = [tex] \pi [/tex](1.09)²(4)
                             = 15 cm³

Your answer will be C. 15 cm³

agamal91
the volume of a cylinder= height * base area
while the base area = [tex] \pi r^{2}[/tex]
since the two cylinders are similar then the ratio between the two radii= the ratio between the two heights =16/4 =4
then the volume of the large cylinder with respect to the smaller dimensions= [tex] \pi * (4r)^{2} *(4*4)=(\pi r^{2} *4)*4*16[/tex]
but [tex] the volume of the smaller one = \pi r^{2} *4[/tex]
then the volume of the large cylinder = the volume of the smaller cylinder*4*16=960
then the smaller's volume= [tex] \frac{960}{4*16}=15[/tex]