CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 15 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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.


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


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.)


For upper conical portion, Radius of the base



For lower conical portion, Volume

For central cylindrical portion

Radius of the base


Volume of the model

Lower Conical Portion
Volume of the Model