The volume of a cube is 125 cubic inches. Find the surface area.
I know that the volume formula is V=Bh where v=volume, B=area of the base, and h=height. How do I get the surface area though?
Also,
The surface area of a cube is 384 square cm. Find the volume.
I think it's basically the same problem. So far, I know 384=Ph+2B, the surface area formula. I don't know how to find the variables though.
The surface area of a cube is 6a^2
a = the length of a side.
It's the area of the 6 squares that cover it.
The volume of a cube is the length of one side cubed.
So let's look at the first example.
125 cubic inches = volume
Let's find the length of one side.
The cube root of 125 is 5.
So one side is 5" long.
So you have 6(5^2)
Multiply it out and see what you get :)
Can you use those formulas above and different information to figure out the second question?
Think it through rather than rely too much on 'formulas'
In a regular cube all sides are equal and all faces are squares.
first of all if the volume is 125, then each side must be 5
(5x5x5 = 125)
Aren't there 6 faces, each a square 5 by 5??
so the area of each face is 25 square cm, there are 6 of them so..
the total surface area is 150 cm^2
In the second part, reverse your steps.
384 is the area of all six faces, so each one is 64 .........
how do you draw a picture with cubes and then have the volume of the pictures
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
512m^3
mjfbugbjfasngdnvjdnfvbwyefbgyfebvhwbivbehfbvhdfvbkfjl
The volume of a cube is given by the formula V = a^3, where a is the length of one side of the cube.
1. In the first example, the volume of the cube is 125 cubic inches. We can find the length of one side by taking the cube root of the volume:
125^(1/3) = 5 inches
Now that we know the length of one side, we can find the surface area of the cube. The surface area formula for a cube is S = 6a^2, where S is the surface area and a is the length of one side:
S = 6(5^2)
S = 6(25)
S = 150 square inches
Therefore, the surface area of the cube is 150 square inches.
2. In the second example, the surface area of the cube is given as 384 square cm. We can find the length of one side by rearranging the surface area formula:
384 = 6a^2
Divide both sides by 6:
384/6 = a^2
64 = a^2
Take the square root of both sides:
√64 = √(a^2)
8 = a
Now that we know the length of one side, we can find the volume of the cube using the volume formula V = a^3:
V = 8^3
V = 512 cubic cm
Therefore, the volume of the cube is 512 cubic cm.
To find the surface area of a cube, we use the formula: Surface Area = 6a^2, where "a" is the length of one side of the cube.
Let's use this formula to solve the first example:
Given: Volume = 125 cubic inches
We know that the formula for the volume of a cube is: Volume = a^3, where "a" is the length of one side.
So in this case, we have 125 = a^3.
To find the value of "a", we take the cube root of both sides: cube root of 125 = cube root of a^3.
So, a = 5 inches. (since 5 x 5 x 5 = 125).
Now that we know the length of one side is 5 inches, we can substitute this value into the surface area formula: Surface Area = 6 x (5^2).
Calculating this gives us: Surface Area = 6 x 25 = 150 square inches.
Therefore, the surface area of the cube is 150 square inches.
Now let's solve the second example:
Given: Surface Area = 384 square cm.
We know that the formula for the surface area of a cube is: Surface Area = 6a^2.
Using this formula, we can rearrange it to solve for "a":
Surface Area = 6a^2
Divide both sides by 6: Surface Area/6 = a^2
Take the square root of both sides: square root of (Surface Area/6) = a.
Now, substitute the given value of Surface Area = 384 square cm into the formula:
a = square root of (384/6).
Calculating this gives us: a = square root of 64 = 8 cm.
Since all sides of a cube are equal, the length of one side "a" is 8 cm.
Now that we know the length of one side, we can use the formula for volume: Volume = a^3.
So, the volume of the cube is: Volume = 8^3 = 512 cubic cm.
Therefore, the volume of the cube is 512 cubic cm.