Q. 44.3( 438 Votes )

# A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Answer :

From the figure:

The greatest diameter possible for the hemisphere is equal to the cube's edge= 7cm

Radius (*r*) of hemispherical part = 7/2cm

The total surface area of solid = Surface area of cubical part + CSA of hemispherical part - Area of the base of hemispherical part

= 6 (Edge)^{2} + 2πr^{2} – πr^{2}

= 6 (Edge)^{2} + πr^{2}

Total surface area of solid = 6 (7)^{2} +( × × )

= 294 + 38.5

= 332.5 cm^{2}

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PREVIOUSA toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.NEXTA hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

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