The sum of the length breadth and height of a cuboid is 6 root 3

Length Width Height The length, width and height are the dimensions of a geometrical figure that depict how long, wide and high a figure is. While length is the longest side of a figure, width is the shorter side and height is the vertical dimension of the figure. Let us learn more about the length width height of figures. 1. 2. 3. 4. What is Length Width Height? Length, width, and height are the tools that are used to find the dimensions of an object. When we refer to two-dimensional shapes ( • Length: Length is used to measure the distance between two points. Length is the longest dimension of a figure and it shows how long the given object or figure is. It is expressed in linear units like meters, centimeters, inches, and so on. • Width: Width is the shorter distance of an object or a figure and it shows how broad or wide the given figure is. Width is also expressed in linear units like meters, centimeters, inches, and so on. • Height or Depth: The height of an object refers to its depth or the third vertical dimension of the object and it shows how high or deep an object is. The height or depth of an object is expressed in linear units like meters, centimeters, inches, and so on. It should be noted that length, width, height and depth are words that are derived from the words long, wide, high, and deep, respectively. Hence they express the dimensions of an object. Observe the figure given below to see the length width and height of a Length vs Width The difference betw...

The sum of the length, breadth and height of a cuboid is `6sqrt(3)` cm and the length of its diagonal is `2sqrt(3)` cm. The total surface area of the cuboid is `underline(bb(96 cm^2)`. Explanation: Let Length = l Breadth = b Height = h Given that Sum of the length, breadth and height of a cuboid is `6sqrt(3)` cm l + b + h = `6sqrt(3)` cm ......(1) Also, given that Length of its diagonal is `2sqrt(3)` cm `sqrt(l^2 + b^2 + h^2) = 2sqrt(3)` ......(2) We need to find Total surface area of the cuboid Now, Total surface area of cuboid = 2(lb + bh + lh) From (1) l + b + h = `6sqrt(3)` cm Squaring both sides (l + b + h) 2 = `(6sqrt(3))^2` l 2 + b 2 + h 2 + 2lb + 2bh + 2lh = `6^2 xx (sqrt(3))^2` l 2 + b 2 + h 2 + 2lb + 2bh + 2lh = 36 × 3 l 2 + b 2 + h 2 + 2lb + 2bh + 2lh = 108 From (1) `sqrt(l^2 + b^2 + h^2) = 2sqrt(3)` Squaring both sides `(sqrt(l^2 + b^2 + h^2))^2 = (2sqrt(3))^2` l 2 + b 2 + h 2 = 2 2× `(sqrt(3))^2` l 2 + b 2 + h 2 = 4 × 3 l 2 + b 2 + h 2 = 12 12 + 2lb + 2bh + 2lh = 108 2lb + 2bh + 2lh = 108 – 12 2lb + 2bh + 2lh = 96 Total surface area = 96 cm 2

Given: (l + b + h) = 40 2(lb + bh + lh) = 992 Formula used: Total surface area = 2(lb + bh + lh) The maximum length of a stick that can placed inside the cuboid box = \(\sqrt \) ⇒√(608) ⇒ 4√38 cm Candidates who have completed Higher Secondary (10+2) can appear for this exam for recruitment to various posts like Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II). To enhance your preparation for the exam, practice important questions from

In our daily life, we see many objects like books, pencil boxes, cones, football, cylinder. These all are three-dimensional objects (solid shapes). All these objects occupy some shape and have three dimensions Length, Breadth, Height, or Depth. We often find some shapes with two or more identical (congruent) faces. For example, the cube has squared faces on each side. Surface Area The surface area of an object is the sum of all the areas of the shapes that cover the surface of the object. For example, the surface area of a cube is the sum of the area of six squares that cover it. If the area of one side is a 2 then the area of six sides is 6a 2 which is its surface area. = 7 m Example 3. What is the surface area of a cube of side 6cm? Solution: Given, Side of cube = a = 6cm Surface Area of cube = 6a 2 = 6 * 6 2 cm 2 = 216 cm 2 Example 4. Find the side of a cube whose surface area is 384 cm 2? Solution: Given, Surface area of a cube = 384 cm 2 Let ‘a’ be the side of a cube . we know that , surface area of cube = 6a 2 => 6a 2 = 384 => a 2= 384 / 6 => a 2= 64 => a = √64 => a = 8 Therefore, side of a cube = 8cm. Note: The lateral surface area of a cube is the Total surface area of a cube, which is equal to the sum of areas of all its sides. Cuboid A cuboid is made up of six rectangular planes, with different values of length, width, and height. It may be a brick or a box which has a rectangular view from aside. A cuboid is a three-dimensional solid with six rectangular faces. ...