CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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