Surface areas and Volumes — Chapter Summary

For a cuboid with length l

For a cuboid with length l, breadth b, and height h: Total Surface Area = 2(lb + bh + lh), Lateral Surface Area = 2h(l + b), Volume = lbh. Example: A

For a cube with edge length

For a cube with edge length s: Total Surface Area = 6s², Lateral Surface Area = 4s², Volume = s³. Example: A cube with edge 4cm has TSA = 6×16 = 96 cm

For a cylinder with radius r

For a cylinder with radius r and height h: Curved Surface Area = 2πrh, Total Surface Area = 2πr(r+h), Volume = πr²h. Example: Cylinder with r=7cm, h=1

For a cone with radius r

For a cone with radius r, height h, and slant height l (where l² = r² + h²): Curved Surface Area = πrl, Total Surface Area = πr(r+l), Volume = (1/3)πr

For a sphere with radius r

For a sphere with radius r: Surface Area = 4πr², Volume = (4/3)πr³. For hemisphere: Curved Surface Area = 2πr², Total Surface Area = 3πr², Volume = (2