Find the lateral surface of a cuboid whose length, breadth and height are in a ratio of 4:3;2 and volume of the cuboid is 5184 cubic metre.
To find the lateral surface area of a cuboid, we need to first determine the dimensions of the cuboid. Given that the length, breadth, and height are in the ratio 4:3:2, we can represent them as 4x, 3x, and 2x, respectively, where x is a common factor.
Next, we can use the formula for the volume of a cuboid to find the value of x. The formula for the volume is given by: Volume = length * breadth * height.
Given that the volume of the cuboid is 5184 cubic meters, we can substitute the respective values in the formula and solve for x:
5184 = (4x) * (3x) * (2x)
Simplifying the equation:
5184 = 24x^3
Dividing both sides by 24:
216 = x^3
Taking the cube root of both sides, we find:
x = 6
Now that we have the value of x, we can calculate the dimensions of the cuboid:
Length = 4x = 4 * 6 = 24 units
Breadth = 3x = 3 * 6 = 18 units
Height = 2x = 2 * 6 = 12 units
The lateral surface area of a cuboid is given by the formula: Lateral Surface Area = 2 * (length * height + breadth * height).
Substituting the known values into the formula, we get:
Lateral Surface Area = 2 * (24 * 12 + 18 * 12)
= 2 * (288 + 216)
= 2 * 504
= 1008 square units.
Therefore, the lateral surface area of the given cuboid is 1008 square units.
4*3*2 = 24
5184/24 = 216 = 6^3
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Or, more usually you will be asked to solve
4x * 3x * 2x * 5184