Respuesta :
Dimensions of cylinder must be multiplied by a factor of [tex]\frac {1} {3}[/tex], to give a similar cylinder and reduce the volume by 208 [tex]cm^3[/tex].
Step-by-step explanation:
Here we have , A cylinder has a volume of 216 [tex]cm^3[/tex]. By what factor must the dimension of the cylinder be multiplied to give a similar cylinder and reduce the volume by 208 [tex]cm^3[/tex] . Let's find out:
We know that Volume of cylinder = [tex]\pi r^2h[/tex]
Now , Similar cylinder means dimensions are in same ratio . According to question initial volume is 216 [tex]cm^3[/tex] i.e.
⇒ [tex]V =216 = \pi r^2h[/tex]
Now , the volume is reduced by 208 [tex]cm^3[/tex] , So new volume is :
⇒ [tex]V_1=216-208[/tex]
⇒ [tex]V_1=8=\pi r_1^2h_1[/tex]
Here , [tex]\frac{V}{V_1} = \frac{r^2h}{r_1^2h_1}[/tex]
⇒ [tex]\frac{216}{8} = \frac{r^2h}{r_1^2h_1}[/tex]
⇒ [tex]27= \frac{r^2h}{r_1^2h_1}[/tex]
⇒ [tex]r_1^2h_1= \frac{r^2h}{27}[/tex]
⇒ [tex]r_1^2h_1= (\frac{r}{3})^2\frac{h}{3}[/tex]
Therefore , Dimensions of cylinder must be multiplied by a factor of [tex]\frac {1} {3}[/tex], to give a similar cylinder and reduce the volume by 208 [tex]cm^3[/tex]
