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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Step-by-step explanation:
Given -:
A toy is in the form of a cone mounted with hemisphere.
Radius of cone = radius of hemisphere = 3.5 cm
height of toy= 15.5 cm
To find -:
Total surface area of toy
Solution -:
- First, We need to find curved surface area of hemisphere.
=> CSA = 2πr²
=2× 22/7× 3.5 × 3.5
= 2 ×22× 0.5 × 3.5
=> CSA of hemisphere = 77 cm²
- Now we need to find CSA of cone, for which we need to find slant height ( L )
height of cone = height of toy-height of hemisphere ( or radius)
=> 15.5 - 3.5
=> 12 cm
Slant height or L = √(h²+ r²)
=> √(12²+3.5²)
=> √156.25 cm ²
=> 12.5 cm
CSA of cone = πrl
=> 22/7×3.5×12.5
=> 22×0.5 × 12.5
=> 11 × 12.5
=> CSA of cone = 137.5 cm²
- Now we need to find the total surface area of the toy
Total surface area of toy = CSA of cone + CSA of hemisphere
=> 137.5 + 77
=> Total surface area of the toy = 214.5 cm²
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