Question

A. 11 cm^3
B. 14 cm^3
C. 15 cm^3
D. 25 cm^3

Answer 1

the volume of a cylinder= height * base area
while the base area =
`\pi r^(2)`
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=
`\pi * (4r)^(2) *(4*4)=(\pi r^(2) *4)*4*16`
but
`the volume of the smaller one = \pi r^(2) *4`
then the volume of the large cylinder = the volume of the smaller cylinder*4*16=960
then the smaller's volume=
`(960)/(4*16)=15`

Answer 2

Lets get started :)

We need to find the radius of the larger cylinder

V =
`\pi`r²h
960 =
`\pi`r²(16)

`(960)/(16) = \pi r^2`
60 =
`\pi r^2`

`(60)/( \pi ) = r^2`
r =
`\sqrt{ (60)/( \pi ) }`
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


`(4.37)/(4)` = r
r = 1.09 cm (radius of small cyclinder)

V (small cylinder) =
`\pi`(1.09)²(4)
= 15 cm³

Your answer will be C. 15 cm³