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Question
The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
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Solution
Let the radius of a toy = r and
height of the toy = h
The curved surface area of a toy = 132 cm2
=> 2πrh = 132 cm2
⇒ `2pirh = 132` cm2
⇒ `r = 132/(2pi xx h)` cm2 ...(i)
Also, volume of a toy = 462 cm3
⇒ `pir^2h = 462` cm3
⇒ `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
- Diameter: 14 cm
- Length (Height): 3 cm
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