Ch 11 covers surface area and volume of all important 3D shapes: cubes, cuboids, cylinders, cones, spheres, and hemispheres. Students learn formulas and apply them to real-world problems.
Cuboid: TSA = 2(lb+bh+hl). Cube: TSA = 6a². Cylinder: CSA = 2πrh, TSA = 2πr(r+h). Cone: CSA = πrl where l = √(r²+h²), TSA = πr(l+r). Sphere: SA = 4πr². Hemisphere: CSA = 2πr², TSA = 3πr².
Cuboid: V = lbh. Cube: V = a³. Cylinder: V = πr²h. Cone: V = ⅓πr²h. Sphere: V = (4/3)πr³. Hemisphere: V = (2/3)πr³. Note: cone volume = ⅓ cylinder volume (same base and height).
Download: https://ncert.nic.in/textbook/pdf/iemh111.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
This can be demonstrated experimentally: filling a cone with water and pouring into a cylinder of same base and height requires exactly 3 conefuls. The proof uses integral calculus, but the relationship V_cone = ⅓V_cylinder holds for all cones.
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