The volume of the box is 900 cubic inches. Find the dimension with a ratio of 1:3:5.
1x * 3x * 5x = 900
15 x^3 = 900
x^3 = 60
x = 3.915
3x = 11.745
5x = 19.574
let the dimensions be x , 3x, and 5x
x(3x)(5x) = 900
15x^3 = 900
x^3 = 60
x = ∛60
dimensions are ∛60 , 3∛60, and 5∛60
or appr. 3.91 , 11.74, and 19.57
check: 3.91*11.74*19.57 = 898.33 close for the approximation I used
however, ∛60*3∛60*5∛60 = exactly 900
wow!!!
thnk you so much damon and reiny for helping
now i knw how to use ratios. tnx a lot:)
To find the dimensions of the box with a ratio of 1:3:5, we can use a system of equations.
Let's assume the three dimensions of the box are x, 3x, and 5x.
The formula for the volume of a box is V = length × width × height. In this case, the volume is given as 900 cubic inches. So, we have the equation:
900 = x × 3x × 5x
Simplifying the equation, we get:
900 = 15x^3
Next, divide both sides of the equation by 15 to isolate x^3:
60 = x^3
To find the value of x, we can take the cube root of both sides:
∛(60) = x
Using a calculator, we find that the cube root of 60 is approximately 3.916.
Therefore, the value of x is approximately 3.916.
To find the dimensions, we can multiply x by the ratio 1:3:5:
Length = 1 × x ≈ 1 × 3.916 ≈ 3.916 inches
Width = 3 × x ≈ 3 × 3.916 ≈ 11.748 inches
Height = 5 × x ≈ 5 × 3.916 ≈ 19.58 inches
So, the dimensions of the box with a ratio of 1:3:5 and a volume of 900 cubic inches are approximately 3.916 inches, 11.748 inches, and 19.58 inches.