Respuesta :
Answer:
Required A. radious of the cylinder is [tex]\frac{15.22653}{\sqrt{h}}[/tex] B. there is no change in radious due to change in height.
Step-by-step explanation:
Given volume of the cylinder is 728, that is we know for a cylinder with height h and radious r, volume V is,
[tex]V=\pi r^2 h[/tex]
A. To find radious of the cylinder :
[tex]\therefore 728=\pi r^2 h[/tex]
[tex]\implies r^2 h=\frac{728}{\pi}[/tex]
[tex]\implies r^2=\frac{728}{3.14 \times h}[/tex]
[tex]\implies r=\sqrt{\frac{728}{3.14\times h}}[/tex]
[tex]\implies r=\frac{15.22653}{\sqrt{h}}\hfill (1)[/tex]
which is the required radious.
B. To find change of radious due to change in height :
If the height h of the cylinder change to [tex]\delta h[/tex] then radious,
[tex]r=\frac{15.22653}{\sqrt{h+\delta h}}[/tex]
From (1) we get,
[tex]r=\frac{15.22653}{\sqrt{h+\delta h}}=\frac{15.22653}{\sqrt{h}}[/tex]
[tex]\implies \frac{1}{\sqrt{h}}=\frac{1}{\sqrt{h+\delta h}}[/tex]
[tex]\implies \sqrt{h}=\sqrt{h+\delta h}[/tex]
Squaring both side we get,
[tex]h=h+\delta h[/tex]
[tex]\delta h=0[/tex]
Which shows that change of height dosen't effect on radious.
