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Question

If a lemon of radius r is divided into four identical parts, then what would be the total surface area of the four parts? (Given Area of a sphere = 4πr2)

A
2πr2
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B
4πr2
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C
6πr2
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D
8πr2
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Solution

The correct option is D 8πr2
We know that,
Surface Area of Sphere = 4πr2
and, the Area of circle = πr2
The cutting of the lemon leads to the creation of new surfaces for each part which must be counted while calculating the total surface area of the four identical parts.
Therefore,
Total Surface Area of the four identical parts,
A = 4 × {(Area of outer curved surface of each part) + (2 × Area of each plane surface i.e semi-circle)}
= 4 × {4πr24 + 2 × πr22 }
= 4 × (πr2+πr2)
= 4 × 2πr2
= 8πr2sq. units,
which is twice the surface area of a single sphere.

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