Find the volume of a rectangular box. The faces have areas of 15, 25, and 60.
factor the areas to see that
15 = 3*5
25 = 5*5
60 = 12*5
Hmm. No obvious integer solutions
15 = 6 * 5/2
25 = 5/2 * 10
60 = 10 * 6
v = 2.5 x 6 x 10 = 150
To find the volume of a rectangular box, you need to know the areas of its faces. In this case, you have three face areas: 15, 25, and 60.
Let's call the length, width, and height of the rectangular box L, W, and H respectively. We can use these values to form three equations using the given face areas.
Equation 1: L * W = 15
Equation 2: W * H = 25
Equation 3: L * H = 60
Now, we need to solve these equations to find the values of L, W, and H. We can start by rearranging the equations:
Equation 1: W = 15 / L
Equation 2: H = 25 / W
Equation 3: H = 60 / L
Since equations 2 and 3 both involve H, we can equate them:
25 / W = 60 / L
Cross-multiplying gives us:
25L = 60W
We can rearrange this equation to solve for W:
W = (25L) / 60
Substituting this value of W into equation 1:
(15 / L) * ((25L) / 60) = 15
Simplifying:
375L² = 900
Dividing both sides by 375:
L² = 900 / 375
L² = 2.4
Taking the square root of both sides:
L ≈ √2.4
Similarly, substituting the value of L into equation 3:
(60 / L) * ((25L) / 60) = 25
Simplifying:
25L = 25
L = 1
We have found the value of L as 1. Substituting this value into equation 1:
W = 15 / (1)
W = 15
Substituting the values of L and W into equation 2:
H = 25 / (15)
H ≈ 1.67
So, the values of L, W, and H are approximately 1, 15, and 1.67 respectively.
Finally, we can calculate the volume of the rectangular box using the formula:
Volume = Length * Width * Height
Volume = 1 * 15 * 1.67
Volume ≈ 25.05 cubic units
Therefore, the volume of the rectangular box is approximately 25.05 cubic units.