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Question
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
Options
2π : 1
4π : 1
3π : 1
1 : 4π
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Solution
The ratio of total surface area of a solid hemisphere to the square of its radius is 3π : 1.
Explanation:
Curved Surface Area = 2πr2
Curved Surface Area of Hemisphere = `(1/2) 4πr^2 = 2πr^2`
Base Area of a hemisphere = πr2
Total Surface Area of Hemisphere = 2πr2 + πr2 = 3πr2
Divide the total surface area by r2
`= (3pir^2)/r^2`
`= 3pi`
Therefore, the ratio of the total surface area of a solid hemisphere to the square of its radius is 3π : 1
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Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
