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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.


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Solution

Given,

Side of a cubical block which is surmounted by a hemisphere =7cm

Here, the greatest diameter the hemisphere can have =Sideofcube=7cm.

Now, Surface area of the solid so formed =T.S.Aofcubicalblock+C.S.Aofhemisphere-Areaofbaseofhemisphere

Step 1: To calculate T.S.A of cubical block

T.S.A of cubical block

=6a2(a=side=7cm)=6×(7)2=6×49=294cm2

Step 2 : To calculate C.S.A of hemisphere

C.S.A of hemisphere

=2πr2(herer=72=3.5cm)=2×227×(3.5)2=2×227×12.25=77cm2

Step 3 : To calculate Area of base of hemisphere

Area of base of hemisphere

=πr2(herer=72=3.5cm)=227×(3.5)2=2×227×12.25=38.5cm2

Step 4: Surface area of the solid so formed

=T.S.Aofcubicalblock+C.S.Aofhemisphere-Areaofbaseofhemisphere=294+77-38.5cm2=332.5cm2

Therefore, the greatest diameter the hemisphere can have is 7cm and the surface area of the solid so formed is 332.5cm2.


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