A top is in the shape of cone over a hemisphere .the radius of the hemisphere is 3.5 cm . the total height of the top is 15.5cm. Find the total area of top? (A) 600 (B) 100 (C) 150 (D) 99
Answers
If the radius of the hemisphere is 3.5 cm and the total height of the top is 15.5 cm, then the total area of the top is 214.5 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 top is in the shape of a cone on a hemisphere.
The radius of the hemisphere, r = 3.5 cm
The total height of the top = 15.5 cm
Step 1:
The height of the cone,
h = [total height of the top] – [radius of the hemisphere] = 15.5 – 3.5 = 12 cm
We know,
The slant height of the cone, l = √[h² + r²] = √[12² + 3.5²] = 12.5 cm
Therefore,
The curved surface area of the conical part of the top = πrl = (22/7) * 3.5 * 12.5 = 137.5 cm²
And,
The curved surface area of the hemisphere part of the top = 2πr² = 2 * 22/7 * 3.5² = 77 cm².
Step 2:
Thus,
The total area of the top is given by,
= [curved surface area of the conical part of the top] + [curved surface area of the hemisphere part of the top]
= 137.5 + 77
= 214.5 cm²
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