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Question

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.


Solution


Given: 
Diameter of hemisphere = Edge of the cube $$= l$$
Radius of hemisphere $$r=\dfrac{l}{2}$$
Total surface area of solid = Surface area of cubical part + Closed Surface of hemisphere part - Area of base of hemispherical part

$$= 6(Edge)^2 + 2\pi r^2 - \pi r^2= 6(Edge)^2+\pi r^2$$

Total surface are of solid = $$6l^2 + \pi \times \left(\dfrac{l}{2}\right)^2$$
= $$6l^2 +\dfrac{\pi l^2}{4}$$

$$ = \dfrac{1}{4}[24+\pi] l^2$$ sq. units

494880_465133_ans.PNG

Mathematics
RS Agarwal
Standard X

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