The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm^{2} and 462 cm^{3} respectively. Find, its diameter and its length.

#### Solution

Let the radius of a toy = r and

height of the toy = h

The curved surface area of a toy = 132 cm^{2}

=> 2πrh = 132 cm^{2}

⇒ `2pirh = 132` cm^{2}

⇒ `r = 132/(2pi xx h)` cm^{2 }......(i)

Also, volume of a toy = 462 cm^{3}

⇒ `pir^2h = 462` cm^{3}

⇒ `r^2 = 462/(pi xx h)` ..........(ii)

Now , substitute the volume of r, we get

`(132)^2/((2)^2 xx (pi)^2 xx h^2) = 462/(pi xx h)`

⇒ `132^2/(4 xx pi xx h) = 462`

⇒ `4 xx pi xx h = (132 xx 132)/462`

⇒ `h = (132 xx 132)/(462 xx pi xx h)`

⇒ `h = (132 xx 132 xx 7)/(462 xx 22 xx 4) = 3` cm

Now, put the value of h in eq. (i), we get

`r = (132 xx 7)/(2 xx 22 xx 3) = 7` cm

∴ Diameter of the toy = `2 xx r`

= `2 xx 7` cm = 14 cm