Question

a toy is in the form of a cone mounted on a hemisphere of radius 3.5cm. If the total height of the toy is 15.5cm ,find its total surface area.

Answer 1

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Answer 2

Total surface area is 214.5 cm²

Radius of the hemisphere = 3.5 cm  (Given)

Height of the toy = 15.5 cm   (Given)

Therefore,

Height of the cone = 15.5 - 3.5 = 12 cm

Slant height of the cone = √h² + r²

= √ 3.5² + 12²

= √ 12.25 + 144

= √ 156.25

= 12.5 cm

Curved surface of hemisphere = 2πr²

= 2 × 22/7 × (3.5)²

= 77 cm²

Lateral surface of cone = πrl

= 22/7 × 3.5 × 12.5

= 137.5 cm²

Total surface area of the toy = CSA of hemisphere + LSA of cone

= 77+137.5

= 214.5

Therefore, the total surface area is 214.5 cm²