Question

The difference between the outer and inner curved surface area of a hollow right circular cylinder $14cm$ long is $88{cm}^2$. If the volume of metal used in making the cylinder is $176{cm}^3$, find the outer and inner diameters of the cylinder. (Use $\pi =22/7$)

Answer 1

Outer curved surface area - Inner curved surface area $=88$

$2\pi r(R-r)=88$

$R-r=\frac{88}{2\times \frac{22}{7}\times 14}$

$R-r=\frac{88\times 7}{2\times 22\times 14}$

$R-r=\mathrm{1........}\left(1\right)$

Also we have

Volume of outer part - Volume of inner part $=176$

$\pi h(R^2-r^2)=176$

$\pi h(R-r)(R+r)=176$

$\pi \times 14(R+r)=176$

$R+r=\frac{176\times 7}{22\times 14}$

$R+r=\mathrm{4......}\left(2\right)$

Adding (1) and (2), we get

$R-r+R+r=5$

$2R=5$

$R=\frac{5}{2}$

$D=5$

Putting in (2)

$\frac{5}{2}+r=4$

$r=4-\frac{5}{2}$

$r=\frac{8-5}{2}$

$r=\frac{3}{2}$

$d=3$