Question

The cylinder shown has a volume of 728 cubic inches. A. What is the radius of the​ cylinder? Use 3.14 for pi. B. If the height of the cylinder is​ changed, but the volume stays the​ same, then how will the radius​ change? Explain.

Answer 1

Answer:

Required A. radious of the cylinder is $\frac{15.22653}{\sqrt{h}}$ 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,

$V=\pi r^2 h$

A. To find radious of the cylinder :

$\therefore 728=\pi r^2 h$

$\implies r^2 h=\frac{728}{\pi}$

$\implies r^2=\frac{728}{3.14 \times h}$

$\implies r=\sqrt{\frac{728}{3.14\times h}}$

$\implies r=\frac{15.22653}{\sqrt{h}}\hfill (1)$

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 $\delta h$ then radious,

$r=\frac{15.22653}{\sqrt{h+\delta h}}$

From (1) we get,

$r=\frac{15.22653}{\sqrt{h+\delta h}}=\frac{15.22653}{\sqrt{h}}$

$\implies \frac{1}{\sqrt{h}}=\frac{1}{\sqrt{h+\delta h}}$

$\implies \sqrt{h}=\sqrt{h+\delta h}$

Squaring both side we get,

$h=h+\delta h$

$\delta h=0$

Which shows that change of height dosen't effect on radious.