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Largest possible sphere is cut from a hemisphere of total surface area 665.28 cm2, then what is the difference between surface area of newly formed sphere and total curved surface area of original hemisphere?

Largest possible sphere is cut from a hemisphere of total surface area 665.28 cm2, then what is the difference between surface area of newly formed sphere and total curved surface area of original hemisphere? Correct Answer 221.76 cm<sup>2</sup>

Given:

Total surface area of hemisphere = 665.28 cm2

Formula Used:

Total surface area of hemisphere = 3πr2

Surface area of sphere = 4πr2

Calculation:

Let the radius of hemisphere be R

Total surface area of hemi-sphere

⇒ 3πR2 = 665.28

⇒ R2 = 70.56

⇒ R = 8.4 cm

Now,

Diameter of largest possible sphere = Radius of hemisphere = 8.4 cm

Radius of sphere = 8.4/2 = 4.2 cm

Surface area of sphere = 4πr2

⇒ 4 × π × (4.2)2

⇒ 221.76 cm2

Curved surface area of hemi-sphere = 665.28 × (2/3)

⇒ Curved surface area of hemi-sphere = 443.52 cm2

⇒ Required difference = 443.52 – 221.76

∴ Required difference = 221.76 cm2

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