#### Question

A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

#### Solution

The diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm.

Therefore, radius=`r=7/2cm`

Its curved surface area=`2pir^2`

`=2xx22/7xx7/2xx7/2`

`=77 cm^2` ......................(1)

Surface area of the top of the resulting solid = Surface area of the top face of the cube − Area of the base of the hemisphere

=`(7xx7)-(22/7xx49/4)`

`=49-77/2`

`=(98-77)/2`

`=21/2`

`= 10.5 cm^2`....................(2)

Surface area of the cube`=5xx("side")^2=5xx49=245 cm^2`

Total area of resulting solid`=245+10.5+77=332.5 cm^2`

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Solution A Cubical Block of Side 7 Cm is Surmounted by a Hemisphere of the Largest Size. Find the Surface Area of the Resulting Solid. Concept: Area and Volume of Solids - Cone.