LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

VOLUME & SURFACE AREA OF CUBOID

**CUBOID –**

**A cuboid is a solid figure bounded by six rectangular faces and is three-dimensional. The adjacent faces are mutually perpendicular and the opposite faces have the same dimension. A cuboid has eight vertices (M, N, O, P, Q, R, S, T) and twelve edges (MN, OP, PM, ON, QR, RS, ST, TQ, MQ, PT, NR, OS). The volume of a cuboid is considered the product of its length, breadth, and height. We would like denoting the volume = V, length = l, breadth = b, and height = h. we have the formula such as -**

**volume (V) = length (l) X breadth (b) X height (h)**

**So, V = l X b X h**

** V V V**

**So, l = ---------- , b = ---------- , h = -----------**

** b X h l X h b X l**

**The surface area of a cuboid is considered as the sum of the surface areas of its six rectangular faces, which works out to the following.**

**As we all know that, area (A) of a rectangle = length (l) X breadth (b) and also know that, every side of a cuboid is a rectangle and the area of a rectangle of every two opposite sides of a cuboid is the same. **

**So, POST = MNRQ = h X l**

** PMQT = ONRS = b X h**

** MNOP = QRST = l X b**

**Now, the surface area of the cuboid **

**= POST + MNRQ + PMQT + ONRS + MNOP + QRST**

**= hl + hl + bh + bh + lb + lb**

**= 2(hl + bh + lb)**

**The lateral surface area or the area of the four walls of a cuboid works out to.**

**The area of the four walls = perimeter of the floor X height**

** = 2(l + b) X h**

**Example) The dimensions of a cuboid are 10 cm by 8 cm by 9 cm. find (1) its volume, (2) it's surface area, (3) the surface area of the four walls.**

**Ans.) Here, l = 10 cm, b = 8 cm, h = 9 cm**

**(1) the volume of the cuboid = l X b X h **

** = 10 cm X 8 cm X 9 cm = 720 cmᶟ (Ans.)**

**(2) its surface area = 2 (lb + bh + hl) **

** = 2 {(10 X 8) + (8 X 9) + (9 X 10)}**

** = 2 (80 + 72 + 90) **

** = 2 X 242 = 484 cm² (Ans.)**

**(3) Surface area of the four walls = 2 (l + b) X h **

** = 2 (10 + 8) X 9**** **

** = (2 X 18) X 9 **** **

** = 36 X 9 = 324 cm² (Ans.)**