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.