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The length of the base diameter of a woo...

The length of the base diameter of a wooden toy of conical shape uis 10 cm . The expenditure for polishing whole surfaces of the toy at the raye of rupees 2.10 per square - metre is rupees 429. Calculate the height of the toy. Also determine the quantity of wood which is required to make the toy.

Text Solution

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The base diameter of the toy `=10cm`.
`therefore` Radius of the base of the toy `=(10)/(2)cm=5cm`.
Let the slant height of the toy `=l cm`.
`therefore` The curved surface area of the toy `=(220)/(7)xx5xxl sq -cm`
rupees 2.10 is expent to polish 1 sq-m of the area .
`therefore "rupees " 1 " is " '' " "''" "''(1)/(2.10)" "''" "''" "''" "''`
`therefore "rupees " 429 " is " '' " "''" "''" "(1xx429)/(2.10) " sq-m of the area"`.
As per condition , `(22)/(7)xx5xxl=(429)/(2.10)rArr l=(429xx7)/(2.10xx22xx5)rArr 1=13`
So, the slant height of the toy `=13cm`.
`therefore h^2+5^2=(13)^2 or , h^2+25=169 or , h^2=169-25or , h^2=144`
`therefore h=sqrt(144)rArr h=12`.
`therefore` the toy `=12cm`
Again , the volume of the toy `=(1)/(3)xx(22)/(7)xx5^2xx12 c c =(2200)/(7)c c = 314(2)/(7)c c`.
Hence , the height of the toy is 12 cm and the quantity of wood required to make the toy is `314(2)/(7)c c`.
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