The surface area of a particular cube is 600 square inches. When the
edges of the cube are doubled in length, what is the volume of the
new cube, in cubic inches?
100 because when you multiply 6 by 100 you will get 600
The volume of two cubes is proportional to the cube of their sides
since you increased the side by a factor of 2
the volume will increase by a factor of 2^3
Can you find the side of the original cube knowing its surface area is 600 ?
Well, well, well, we have ourselves a cube conundrum, don't we? Let me put on my clown nose and help you out!
The surface area of a cube is given by the formula 6s^2, where s is the length of its edges. So, in this case, we have 6s^2 = 600 square inches. Solving for s, we find that s = √(100) = 10 inches.
Now, when we double the length of the edges, each edge becomes 2s = 2 * 10 = 20 inches. And since all the edges of a cube are equal, we know that the length, width, and height of our new cube are all 20 inches.
And ta-da! The volume of a cube is given by the formula s^3, so the volume of our new cube is 20^3 = 8000 cubic inches. So, the volume of the new cube is 8000 cubic inches. Enjoy your supersized cube!
To find the surface area of a cube, you use the formula:
Surface Area = 6 * side^2
Given that the surface area of the original cube is 600 square inches, we can set up the equation:
600 = 6 * side^2
Dividing both sides by 6:
100 = side^2
Taking the square root of both sides:
side = sqrt(100)
side = 10 inches
Now, if we double the length of each side of the cube, the new side length becomes 2 * 10 = 20 inches.
To find the volume of the new cube, we use the formula:
Volume = side^3
Substituting the new side length, we get:
Volume = 20^3
Volume = 8000 cubic inches
Therefore, the volume of the new cube is 8000 cubic inches.
To find the volume of the new cube, we first need to determine the length of its edges. Since the edges of the original cube have been doubled in length, let's call the length of each edge of the original cube "x". Therefore, the edges of the new cube would have a length of "2x".
Now that we have determined the length of the edges of the new cube, we can calculate its volume. The volume of a cube is given by the formula:
Volume = (side length)³
In this case, the side length of the new cube is "2x". Substituting this value into the formula:
Volume = (2x)³
Volume = 8x³
Therefore, the volume of the new cube is 8x³ cubic inches.
To find the value of "x", we need to start with the original cube's surface area and work backwards.
The surface area of a cube is given by the formula:
Surface Area = 6(side length)²
In this case, the surface area of the original cube is given as 600 square inches. So we can write the equation:
600 = 6x²
Simplifying the equation by dividing both sides by 6:
100 = x²
Taking the square root of both sides to solve for "x":
√100 = √(x²)
10 = x
Now that we have found the value of "x", we can substitute it into the formula for the volume of the new cube:
Volume = 8x³
Volume = 8(10)³
Volume = 8(1000)
Volume = 8000 cubic inches
Therefore, the volume of the new cube is 8000 cubic inches.