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Deepak Bora
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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.

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This question was asked in 2012 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 829, exercise 17D, problem number 35

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  1. ht of toy=15.5 cm (given)

    ht of hemisphere=3.5 cm

    ht of cone=15.5-3.5

    =12cm

    slant ht. of cone=under root h^2+r^2

    =under root (12^2+3.5^2)

    =under root 144+12.25

    =under root 156.25

    = 12.5 cm

    CSA oc hemisphere=2×22/7×(3.5)^2

    =77 cm^2

    CSA of cone=22/7×3.5×12.5

    =137.5 cm^2

    TSA of toy=CSA of hemisphere+CSA of cone

    =77+137.5

    =214.5cm^2

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