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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. - Mathematics

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Sum

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)` cm......(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

Concept: Surface Area of a Cuboid
  Is there an error in this question or solution?

APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 21 Surface Area, Volume and Capacity
Exercise 21 (E) | Q 5 | Page 244
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