A box has a volume of 7500 cm3 and a surface area of 2600 cm2. What are length, width, and height of the box?
L*W*H=7500
2(L*W+L*H+W*H)=2600
This system has an infinite number of solutions and one of them is:
L=30, W=25, H=10
Thank you so much!
correct
30 x 20 x 10 doesn't fit the surface area
What about surface area?
They said something about the surface area where is that?
i needed this, thank you
I did not understand
for the whole numbers only one combination exists: 30 25 10
The way to solve it is to look at 7500, 00 at the end indicates that at least 2 numbers needs to end with 0 ;
simplest 10 750 (10 75) will result in incorrect SA
20 375 (75 5 ,15 25) will result in incorrect SA
30 250 (25 10) matches SA
To find the dimensions of the box, we need to set up a system of equations using the given information.
Let's assume the length, width, and height of the box are represented by L, W, and H respectively.
1. The volume of the box is given by the formula:
Volume = Length x Width x Height
So, we have the equation: L x W x H = 7500 ..........(Equation 1)
2. The surface area of the box is given by the formula:
Surface Area = 2(LW + LH + WH)
Since we know the surface area, we can substitute the values and simplify the equation:
2600 = 2(LW + LH + WH)
2600 = 2LW + 2LH + 2WH
1300 = LW + LH + WH .................(Equation 2)
Now, we have a system of equations (Equation 1 and Equation 2) that can be solved simultaneously.
One way to solve this system is by substitution. We can solve Equation 1 for L and substitute the value of L in Equation 2 to find the values of W and H.
From Equation 1:
L = 7500 / (W x H) ..........(Equation 3)
Now, substitute Equation 3 into Equation 2:
1300 = (7500 / (W x H)) x W + (7500 / (W x H)) x H + WH
Simplifying further:
1300 = 7500 / H + 7500 / W + WH ...........(Equation 4)
Now, rearrange Equation 4 so that one side is equal to zero:
WH - (1300 - 7500 / H - 7500 / W) = 0
This equation is a quadratic equation in terms of W and H. Solving this equation will give us the values of W and H. Once we have the values of W and H, we can substitute them into Equation 3 to solve for L.
Please note that solving this quadratic equation might involve using numerical methods or approximations, depending on the values involved.