Respuesta :
Option C
The ratio for the volumes of two similar cylinders is 8 : 27
Solution:
Let there are two cylinder of heights "h" and "H"
Also radius to be "r" and "R"
[tex]\text { Volume of a cylinder }=\pi r^{2} h[/tex]
Where π = 3.14 , r is the radius and h is the height
Now the ratio of their heights and radii is 2:3 .i.e
[tex]\frac{\mathrm{r}}{R}=\frac{\mathrm{h}}{H}=\frac{2}{3}[/tex]
Ratio for the volumes of two cylinders
[tex]\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{\pi r^{2} h}{\pi R^{2} H}[/tex]
Cancelling the common terms, we get
[tex]\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{\mathrm{r}}{R}\right)^{2} \times\left(\frac{\mathrm{h}}{\mathrm{H}}\right)[/tex]
Substituting we get,
[tex]\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{2}{3}\right)^{2} \times\left(\frac{2}{3}\right)[/tex]
[tex]\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{2 \times 2 \times 2}{3 \times 3 \times 3}[/tex]
[tex]\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{8}{27}[/tex]
Hence, the ratio of volume of two cylinders is 8 : 27
