A rectangular prism has a square base with area 4 m2
.
The surface area of the prism is 48 m2
.
What are the dimensions of the prism?
so the base is 2x2, with perimeter=8
2*4 + 8h = 48
h = 5
so the prism is 2x2x5
2 * 2 * 5
Shouldn't it be 2x4 then times 6 because the number of faces??
it still equals 48m2
To find the dimensions of the rectangular prism, we need to understand the formula for surface area and the relationship between the base and the sides of the prism.
The surface area of a rectangular prism is calculated by adding up the areas of all its faces. For a rectangular prism, we have 6 faces - the top and bottom, and the four sides.
Since the base of the prism is a square, we know its area is 4 m^2. Given that the surface area of the prism is 48 m^2, we can start by subtracting the area of the base from the total surface area to find the combined area of the four sides.
Surface area of the prism - Area of the base = Area of the four sides
48 m^2 - 4 m^2 = 44 m^2 (Area of the four sides)
Since there are four sides, we divide the combined area of the four sides by 4 to find the area of each side:
44 m^2 / 4 = 11 m^2 (Area of each side)
Now, let's consider the sides of the prism. Since the base is a square, the two sides adjacent to the base are also squares. Therefore, their areas would also be 4 m^2 each.
Area of each side - Area of one square side = Area of the remaining two sides
11 m^2 - 4 m^2 = 7 m^2 (Area of the remaining two sides)
Now, we have the area of one side of the prism (7 m^2), which is also the area of the other side since they are the same. This means that each side has an area of 7 m^2.
To find the dimensions of the prism, we need to find the length of the sides. Since it is a rectangular prism, we need two dimensions: length (l) and width (w). Since both sides are squares, the length and width are equal.
Therefore, we can find the length and width by finding the square root of the area of one side (7 m^2):
Length = Width = √(Area of one side) = √(7 m^2) ≈ 2.65 m
So, the dimensions of the rectangular prism are approximately 2.65 m by 2.65 m by 2.65 m.