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Mathematics

Find

(i) the curved surface area.

(ii) the total surface area of a hemisphere of radius 21 cm.

Mensuration

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Answer

(i) Given, radius = 21 cm.

Curved surface area of hemisphere = 2πr2.

Putting values in equation we get,

Curved surface area of hemisphere =2×227×(21)2=2×22×4417=194047=2772 cm2.\text{Curved surface area of hemisphere } = 2 \times \dfrac{22}{7} \times (21)^2 \\[1em] = \dfrac{2 \times 22 \times 441}{7} \\[1em] = \dfrac{19404}{7} = 2772 \text{ cm}^2.

Hence, the curved surface area of hemisphere = 2772 cm2.

(ii) Total surface area of hemisphere = 3πr2.

Putting values in equation we get,

Total surface area of hemisphere = 3 x 227\dfrac{22}{7} x (21)2

=3×22×4417=291067=4158 cm2.= \dfrac{3 \times 22 \times 441}{7} \\[1em] = \dfrac{29106}{7} = 4158 \text{ cm}^2.

Hence, the total surface area of hemisphere = 4158 cm2.

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