A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.
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Given –
Total Height of cone = 31 cm
Radius of hemisphere(r) = Base Radius of Cone
= Height of hemisphere
= 7 cm
∴ Height of cone(h) = 31 – 7 = 24 cm
Slant Height of Cone(l) = √(h2 + r2) = √(242 + 72) = 25 cm
Now,
Total Surface Area of the Toy
= Curved Surface Area of Cone + Curved Surface Area of Hemisphere
= πrl + 2πr2
= π(rl + 2r2)
= π(7 × 25 + 2 × (7)2)
= π(175 + 98)
= π(273)
= 3.14 × 273
= 857.22 cm2
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