A cuboid has total surface area 149square meter and lateral surface area is 135 square meter.find its base
Well, the figure has six faces, 4 of which are lateral. So, the remaining two faces have an area of 14 m^2.
So, the base must have an area of 7 m^2.
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To find the base of the cuboid, we need to determine the length, width, and height of the cuboid.
Let's start by understanding the concepts involved. A cuboid has six rectangular faces. The total surface area of a cuboid is the sum of the areas of all its faces. The lateral surface area of a cuboid refers to the combined area of the four side faces, excluding the top and bottom faces.
Given that the total surface area of the cuboid is 149 square meters and the lateral surface area is 135 square meters, we can set up the following equations:
Total Surface Area of Cuboid = 2(length × width + width × height + length × height)
Lateral Surface Area of Cuboid = 2(height × width + height × length)
Substituting the given values, we have:
149 = 2(length × width + width × height + length × height)
135 = 2(height × width + height × length)
Now, we can solve these equations simultaneously to find the values of length, width, and height.
Step 1: Divide the above equations by 2 to simplify the calculations:
74.5 = length × width + width × height + length × height
67.5 = height × width + height × length
Step 2: Rearrange the first equation to isolate length:
74.5 - width × height = length × (1 + height)
Step 3: Substitute the value of length from the rearranged equation into the second equation:
67.5 = height × width + (74.5 - width × height) × height
Step 4: Simplify the equation:
67.5 = height × width + 74.5 × height - width × height^2
Step 5: Rearrange the equation to isolate width:
width = (67.5 - 74.5 × height) / (height - height^2)
Step 6: Substitute different values for height (0, 0.1, 0.2, 0.3, ...) into the above equation to obtain corresponding values for width.
For example, let's substitute height = 0.1:
width = (67.5 - 74.5 × 0.1) / (0.1 - 0.1^2)
width = 65 / 0.09
width ≈ 722.22
Repeat this step for various values of height to find corresponding values of width. Each time you substitute a value for height, you will obtain a corresponding value for width.
By repeating the calculations and substituting different values for height, you can find a suitable set of values for length, width, and height that satisfy both equations.