A toy is in the shape of the cone over a hemisphere of radius 8 cm.if the total height of the toy is 14 cm, then what is the total surface area of the toy?
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A toy is in the shape of the cone over a hemisphere of radius 8 cm.if the total height of the toy is 14 cm, then what is the total surface area of the toy?
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Hey buddy ,as , total height of toy = 14 cm
we know that , radius of a hemisphere is its height , so , height of hemisphere = 8 cm
height of cone = total height - height of hemisphere
since , open portion of hemisphere will be the base of cone ,
hence , radius of cone = radius of hemisphere = 8cm
=> height of cone = 14-8 = 6 cm
slant height of cone = √(r²+h²) = √(64+36)= √ 100 = 10 cm.
total surface area of toy = CSA of cone + CSA of hemisphere
=> TSA of toy = πrl + 2πr²
=> TSA of toy = (22/7 × 8 × 10) + (2×22/7×8×8)
=> TSA of toy = {22/7×8×10} + {2×22/7×8×8}
=> TSA of toy = (1760/7)+(44×64/7)
=> TSA of Toy = 251.4 cm² + (402.2) cm²
=> TSA of toy= 653.6 cm² (approx)
hope this helps