Q. 54.0( 392 Votes )

# A 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.

Answer :

According to the question,

Diameter of hemisphere = Edge of cube

= *l*

Radius of hemisphere =

**Curved Surface Area of hemisphere = 2 π r**

^{2}**Surface Area of cube = 6(Edge)2**

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}

TSA of Solid = 6l^{2} + π x ()^{2}

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PREVIOUSA 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.NEXTA medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

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