Mathematics
Assertion (A): The radius of a hemisphere increases from r cm to 2r cm. The ratio between the surface area of the original hemisphere and the resulting hemisphere is 1 : 4.
Reason (R): Surface area of the first case = πr2 + 2πr2
Surface area of the second case = π(2r)2 + 2π(2r)2
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
Mensuration
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Answer
Let A1 be the surface area of the original hemisphere.
A1 = πr2 + 2πr2 = 3πr2.
Let A2 be the surface area of the resulting hemisphere.
A2 = π(2r)2 + 2π(2r)2
= 3π(2r)2
= 3π x 4r2
= 12πr2.
Ratio between the surface area of the original hemisphere and the resulting hemisphere is :
∴ Both A and R are true, and R is the correct reason for A.
Hence, option 3 is the correct option.
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Related Questions
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Reason (R): Required ratio = πr2 x 2r : πr3
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