A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of a cone are 8 CM and 3 CM respectively. Determine the surface area of the toy
Answers
The surface area of the toy which is in the form of a cone mounted on a hemisphere is 163.42 cm² .
Step-by-step explanation:
Required Formulas:
- Curved Surface area of the Cone = πrl
- Curved Surface area of the Hemisphere = 2πr²
It is given that,
A toy is in the shape of a cone on a hemisphere
The diameter of the base, d = 8 cm
So, the radius, r = d/2 = 8/2 = 4 cm
The height of the cone, h = 3 cm
Step 1:
We know,
The slant height of the cone, l = √[h² + r²] = √[3² + 4²] = 5 cm
Therefore,
The curved surface area of the conical part of the toy is,
= πrl
= (22/7) * 4 * 5
= 62.85 cm²
And,
The curved surface area of the hemisphere part of the toy is,
= 2πr²
= 2 * (22/7) * 4²
= 100.57 cm²
Thus,
The total surface area of the toy is given by,
= [C.S.A of the conical part of the toy] + [C.S.A of the hemisphere part of the top]
= 62.85 + 100.57
= 163.42 cm²
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