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Question

A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid (in cm2).

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Solution

The hemisphere surmounts the cube, the maximum diameter the hemisphere can have = side of cube as shown in the figure below. The hemisphere will just touch the sides of top face of the cube.

Therefore, maximum diameter Hemisphere can have = 7 cm

Radius of Hemisphere = r = 72=3.5 cm



Surface area of solid = Surface area of 5 Faces of cube + Surface area of Hemisphere + Surface area left uncovered on the top face of the cube (shown in blue)

=5l2+2.π.r2+ Area of Square ABCD - Area of inscribed circle in square ABCD

=(5×7×7)+(2×227×3.5×3.5)+(49(227×3.5×3.5))

=245+77+(4938.5)=322+10.5=332.5 cm2

The surface area of combined solid = 332.5 cm2


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