consider a cube with side length x cm. what is the volume of the cube?
what is the surface area of the cube?
The material to make the base costs $5/m^2 while it costs $3/m^2 to make the rest of the cube. Write an expression for the cost of material for the whole cube.
cost=5x^2+5*3x^2
To find the volume of a cube, we use the formula V = s^3, where V represents the volume and s represents the side length of the cube.
In this case, the side length of the cube is given as x cm. So, the volume of the cube can be calculated as V = x^3 cm^3.
To find the surface area of a cube, we use the formula SA = 6s^2, where SA represents the surface area and s represents the side length of the cube.
In this case, the side length of the cube is still x cm. So, the surface area of the cube can be calculated as SA = 6x^2 cm^2.
Now, let's move on to determining the cost of materials for the cube.
Given that the base costs $5/m^2 and the rest of the cube costs $3/m^2, we need to find the cost for the whole cube.
To calculate the cost of the base, we need to find the area of the base, which is equal to the side length squared. So, the cost of the base is 5 * x^2.
To calculate the cost of the rest of the cube, we need to find the remaining surface areas (excluding the base) and multiply them by $3/m^2, which can be expressed as 3 * (6x^2 - x^2). Simplifying this expression gives us 3 * 5x^2 = 15x^2.
Finally, to find the total cost for the whole cube, we add the cost of the base to the cost of the rest of the cube. Thus, the expression for the cost of material for the whole cube is 5x^2 + 15x^2 = 20x^2.