Mensuration

Volume = (1/3)πr²h, Curved surface area = πrl, Total surface area = πr² + πrl, Slant height l = √(r² + h²)

For a cone: Volume = (1/3)πr²h, CSA = πrl, TSA = πr² + πrl, and slant height l = √(r² + h²). The formula πr²h is for cylinder volume, not cone.

12 cm

Using Pythagorean theorem: h² + r² = l², so h² = l² - r² = 13² - 5² = 169 - 25 = 144, therefore h = 12 cm

Total surface area ≠ sum of individual surface areas, Some surfaces become internal and are not counted, Volume = sum of individual volumes, Contact surfaces must be subtracted

In combination solids, surfaces that come in contact become internal and are not part of total surface area. However, volume is always the sum of individual volumes.

216 cm²

Total surface area of cube = 6a² = 6 × 6² = 6 × 36 = 216 cm²