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= $\frac{960}{4*16}=15$

Answer 2

Lets get started :)

We need to find the radius of the larger cylinder

V = $\pi$r²h
960 = $\pi$r²(16)
$\frac{960}{16} = \pi r^2$
60 = $\pi r^2$
$\frac{60}{ \pi } = r^2$
r = $\sqrt{ \frac{60}{ \pi } }$
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

$\frac{4.37}{4}$ = 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