Write an equation to solve each problem.
The sides of one cube are twice as long as the sides of a second cube. What is the side length of each cube if the total volume of the cubes is 72 cm^3?
Would it be, 3x+6x=72? Thanks
No. It wouldn't be that.
volumes of cubes is V=s^3 where s is side length.
72= s^3+ (2s)^3= s^3+8s^3
72=9s^3
and you find s, the side length of the smaller cube, and 2s is the side length of the larger cube.
I came up with 8=s^3, how would I solve this? Thanks
Take the cube root of each side.
Thanks for your help!
To solve this problem, we will use the formula for finding the volume of a cube, which is given by side length cubed.
Let's assume that the side length of the second cube is x cm. According to the problem, the sides of the first cube are twice as long as the sides of the second cube. Therefore, the side length of the first cube will be 2x cm.
Now, we can calculate the volume of each cube:
- Volume of the first cube = (2x)^3 = 8x^3 cm^3
- Volume of the second cube = x^3 cm^3
According to the problem, the total volume of the cubes is 72 cm^3. So, we can set up the equation:
8x^3 + x^3 = 72
Combining like terms:
9x^3 = 72
Dividing both sides by 9:
x^3 = 8
To solve for x, take the cube root of both sides:
∛(x^3) = ∛(8)
Simplifying further:
x = 2
Therefore, the side length of the second cube is 2 cm, and since the sides of the first cube are twice as long, the side length of the first cube is 2 * 2 = 4 cm.