DBSE | Class 9Th | THREE DIMENSIONAL (3-D): PRISMS.

THREE DIMENSIONAL (3-D): PRISMS.

🌺🌺🌺🪷🪷 Vinjeet Vedic Maths 🪷🪷🌺🌺

For Cube

𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 = 𝑏𝑎𝑠𝑒 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 × ℎ𝑒𝑖𝑔ℎ𝑡

𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 = 𝐿𝑆𝐴 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑜𝑡ℎ 𝑏𝑎𝑠𝑒𝑠

For Cube

★ If 𝑎 𝑖𝑠 𝑠𝑖𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑢𝑏𝑒

𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 (LSA) 𝑜𝑓 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 Cube = 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 of  base × ℎ𝑒𝑖𝑔ℎ𝑡

𝐿𝑆𝐴 𝑜𝑓 𝑐𝑢𝑏𝑒 = 4𝑎. 𝑎 

                         = 4𝑎²

★ 𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 Cube = 𝐿𝑆𝐴 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑜𝑡ℎ 𝑏𝑎𝑠𝑒𝑠

★ 𝑇𝑆𝐴 𝑜𝑓 𝑐𝑢𝑏𝑒 = 4𝑎² + 2𝑎²

                          = 6𝑎²

★ 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑝𝑟𝑖𝑠𝑚 Cube = 𝑏𝑎𝑠𝑒 𝑎𝑟𝑒𝑎 × 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑟𝑖𝑠𝑚

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐶𝑢𝑏𝑒 = 𝑎² × 𝑎 

                            = 𝑎³

🌺🌺🌺🪷🪷 Vinjeet Vedic Maths 🪷🪷🌺🌺

For Cuboid

★ If l, b & h are respectively length, breadth and height of the cuboid.

𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 (LSA) 𝑜𝑓 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 Cuboid = 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 of  base × ℎ𝑒𝑖𝑔ℎ𝑡

𝐿𝑆𝐴 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑 = 2(𝑙 + 𝑏) × ℎ 

                         = 2(𝑙 + 𝑏) ℎ 

★ 𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑝𝑟𝑖𝑠𝑚 Cuboid = 𝐿𝑆𝐴 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑜𝑡ℎ 𝑏𝑎𝑠𝑒𝑠

𝑇𝑆𝐴 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑 = 2(𝑙 + 𝑏)ℎ + 2𝑙𝑏 

                        = 2lh + 2bh + 2lb

                        = 2𝑙𝑏 + 2𝑏ℎ + 2𝑙ℎ

                        = 2(𝑙𝑏 + 𝑏ℎ + 𝑙ℎ)

★ 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑝𝑟𝑖𝑠𝑚 Cuboid = Area of base × 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑟𝑖𝑠𝑚

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐶𝑢𝑏𝑒 = l × b × h 

                            = l b h

🌺🌺🌺🪷🪷 Vinjeet Vedic Maths 🪷🪷🌺🌺

For Cylinder

If r is radius and h is the height of right

cylinder

★ 𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 (LSA) 𝑜𝑓 𝑎 𝑟𝑖𝑔ℎ𝑡 Cylinder = 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 of base × ℎ𝑒𝑖𝑔ℎ𝑡

𝐿𝑆𝐴 𝑜𝑓 𝑐𝑢𝑏𝑜𝑖𝑑 = 2 π r × ℎ 

                         = 2 π r ℎ 

★ 𝑇𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 Cylinder = 𝐿𝑆𝐴 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑜𝑡ℎ 𝑏𝑎𝑠𝑒𝑠

𝑇𝑆𝐴 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 2 π 𝑟 ℎ + 2 π 𝑟² 

                           = 2 π 𝑟 (ℎ + 𝑟)

★ 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑝𝑟𝑖𝑠𝑚 Cylinder = Area of base × 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 Cylinder

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐶𝑢𝑏𝑒 = l × b × h 

                            = l b h

🌺🌺🌺🪷🪷 Vinjeet Vedic Maths 🪷🪷🌺🌺