The Dimension of a cuboid Are in the Ratio 4:3:1 and its total surface area is 950 cm2 .Find Its Dimensions.
let the sides be 4x , 3x, and x
2(4x)(x) + 2(4x)(3x) + 2(x)(3x) = 950
8x^2 + 24x^2 + 6x^2 = 950
38x^2 = 950
x^2 = 25
x = 5
the sides are 20 cm, 15 cm and 5 cm
To find the dimensions of the cuboid, we can use the fact that the dimensions are in the ratio of 4:3:1.
Let's assume the ratio is 4x:3x:x, where x is a constant.
The total surface area of a cuboid is given by the formula:
2(lw + lh + wh)
We are given that the total surface area is 950 cm². Substituting the dimensions in terms of x into the formula, we get:
2[(4x)(3x) + (4x)(x) + (3x)(x)] = 950
Simplifying the equation:
2[12x² + 4x² + 3x²] = 950
2(19x²) = 950
38x² = 950
x² = 950/38
x² = 25
x = √25
x = 5
Now, we can find the dimensions of the cuboid by substituting the value of x into the ratio:
Length = 4x = 4(5) = 20 cm
Width = 3x = 3(5) = 15 cm
Height = x = 5 cm
Therefore, the dimensions of the cuboid are: 20 cm, 15 cm, and 5 cm.
To find the dimensions of the cuboid, we need to use the given information about the ratio and total surface area.
Let the dimensions of the cuboid be 4x, 3x, and x, where x is a common factor.
The total surface area of a cuboid is given by the formula:
TSA = 2(lw + lh + wh)
Substituting the given ratio into the formula, we have:
950 = 2(4x * 3x + 4x * x + 3x * x)
Expanding and simplifying:
950 = 2(12x^2 + 4x^2 + 3x^2)
950 = 2(19x^2)
950 = 38x^2
x^2 = 950/38
x^2 = 25
x = √25
x = 5
Now, we can find the dimensions of the cuboid:
Length (l) = 4x = 4 * 5 = 20 cm
Width (w) = 3x = 3 * 5 = 15 cm
Height (h) = x = 5 cm
Therefore, the dimensions of the cuboid are 20 cm, 15 cm, and 5 cm.