Ch 12 extends mensuration to combinations of basic solids (e.g., cylinder topped with cone), conversion between shapes (melting and recasting), and introduces the frustum of a cone.
Real objects are often combinations of basic shapes (e.g., a tent = cylinder + cone). For TSA: add individual surface areas minus the shared surfaces. For volume: add individual volumes.
When a solid is melted and recast into another shape, the volume remains constant. Use: Volume of original = Volume of new shape. Example: a cone melted into a sphere.
A frustum is formed by cutting a cone with a plane parallel to the base. Slant height l = √[h²+(r₁−r₂)²]. CSA = π(r₁+r₂)l. TSA = CSA + π(r₁²+r₂²). Volume = πh/3(r₁²+r₂²+r₁r₂).
Download: https://ncert.nic.in/textbook/pdf/jemh112.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
A frustum is the portion of a cone between its base and a cut made by a plane parallel to the base. It looks like a bucket or flower pot — with two circular ends of different radii.
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