With reference to the figure given a alongside, a metal container in the form of a cylinder is surmounted by a hemisphere of the same radius.

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asked Mar 18 in Class X Maths by navnit40 (-3,424 points)

With reference to the figure given a alongside, a metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius 3.5 m. Calculate :

(i) The total area of the internal surface, excluding the base;

(ii) The internal volume of the container in m3.(Take π = 22/7)

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answered Mar 18 by priya12 (-11,688 points)

(i) Total area of the internal surface, encluding base

= 2πrh + 2πr2 , where r = 3.5 m, h = 7 m

= 2 πr(h + r)

= 2 × 22/7 × 3.5 × (7 + 3.5) m2

= (2 × 22/7 × 3.5 × 10.5) m2

= 231 m2

(ii) Internal volume of the container = πr2h + 2/3πr3

= 1/3 × 22/7 ×3.5×  3.5 (21 + 7) m3

= (1/3 ×22/7× 3.5 ×3.5 ×28)m3

= 359.33 m3

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