The dimension of a closed cuboid box are in the ratio 5:4:3 if the total surface area is 0.94m^2,find the dimension of the box.
Wronge
To find the dimensions of the cuboid box, we can follow these steps:
Step 1: Write down the ratios of the dimensions.
The given ratio of the dimensions of the box is 5:4:3.
Step 2: Assign variables to the ratios.
Let's assign variables to the ratios of the dimensions. Let's say the three dimension ratios are 5x, 4x, and 3x.
Step 3: Calculate the total surface area of the cuboid.
The total surface area (TSA) of a cuboid can be calculated by the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the cuboid, respectively.
Given that the total surface area is 0.94 m^2, we can set up the equation:
2(5x)(4x) + 2(5x)(3x) + 2(4x)(3x) = 0.94
Simplifying the equation, we get:
40x^2 + 30x^2 + 24x^2 = 0.94
94x^2 = 0.94
x^2 = 0.01
x = 0.1
Step 4: Calculate the dimensions of the cuboid.
Since we have found the value of x, we can substitute it back into the ratios of the dimensions to find their values.
Length = 5x = 5 * 0.1 = 0.5 m
Width = 4x = 4 * 0.1 = 0.4 m
Height = 3x = 3 * 0.1 = 0.3 m
Therefore, the dimensions of the cuboid box are 0.5 m, 0.4 m, and 0.3 m.
Please check ur annwer again
Awarsome
length 5x
ends 4x by 3x
two sides 5x by 4x -->2*5x*4x = 40x^2
top and bottom 5x by 3x --> 2*5x*3x = 30x^2
two ends 2*4x*3x =24x^2
so
94 x^2 = .94
x^2 = .01
x = .1
.5 * .4 * .3