CBSE Class 10-Mathematics: Chapter –13 Surface Areas and Volumes Part 15
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Question 3:
A cubical block of side is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Answer:
Greatest diameter of the hemisphere Side of the cubical block
TSA of the solid = External surface area of the cubical block CSA of hemisphere
Question 4:
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
Answer:
Diameter of the hemisphere , therefore radius of the hemisphere
Also, length of the edge of the cube
Surface area of the remaining solid
Question 5:
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is and its length is . If each cone has a height of , find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Answer:
For upper conical portion, Radius of the base
Height
Volume
For lower conical portion, Volume
For central cylindrical portion
Radius of the base
Height
Volume of the model
Lower Conical Portion
Volume of the Model