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प्रश्न
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =`22/7`]
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
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उत्तर
Radius of hemisphere = 3.5 cm
total height of the toy = 15.5 cm.
Surface area of cone `=pirl`
`l = sqrt((12)^2 + (3.5)^2)`
`= sqrt156.25`
`=12.5 cm`
Therefore,
Surface area of cone
`= 22/7 xx 3.5 xx 12.5`
`=137.5 cm^2`
Surface area of hemisphere `=2pir^2`
`= 2 xx 22/7 xx 3.5 xx 3.5`
`= 77 cm^2`
Therefore,
Total surface area of the toy
`=137.5 + 77`
`=214.5 cm^2`
Volume of cone
`=1/3pir^2h`
`=1/3 xx 22/7 xx (3.51^2 xx 12)`
`=154 cm^2`
Volume of hemisphere
`=2/3pir^3`
`= 2/3 xx 22/7 xx (3.5)^3`
`= 89.83 cm `
Therefore,
Total volume of the toy
`= (154 + 89.83) cm^3`
`= 243.83 cm^3`
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Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
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