#### Question

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. [Use π = 22/7]

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#### Solution

From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e., 7cm.

Radius (*r*) of hemispherical part = 7/2 = 3.5cm

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part

= 6 (Edge)^{2} + 2πr^{2} - πr^{2} = 6 (Edge)^{2} + πr^{2}

Total surface area of solid = `6(7)^2 + 22/7 xx 7/2xx 7/2`

= 294 + 38.5 = 332.5 cm^{2}

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#### Reference Material

Solution for question: 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. concept: null - Surface Area of a Combination of Solids. For the course CBSE