The missing length x is 8 cm.
The surface area of a cuboid is the sum of the areas of its six faces.
In this case, we are given that the surface area is 70 square centimeters, and we need to find the length x.
Here's how we can solve for x:
Identify the known dimensions: We are given that the height of the cuboid is 3 cm and the width is 1 cm.
Express the areas of the faces in terms of x: We can see that the cuboid has two faces with dimensions 3 cm x 1 cm, two faces with dimensions 1 cm x x cm, and two faces with dimensions 3 cm x x cm.
Therefore, the areas of the faces can be expressed as:
2 faces: 3 cm * 1 cm = 3 cm²
2 faces: 1 cm * x cm = x cm²
2 faces: 3 cm * x cm = 3x cm²
Set up the equation: Now, we can set up the equation for the total surface area:
Total surface area = 2 (3 cm²) + 2 (x cm²) + 2 (3x cm²) = 70 cm²
Solve for x: Simplifying the equation, we get:
6 + 2x + 6x = 70
8x = 64
x = 8
Therefore, the missing length x is 8 cm.
Alternatively, you can also use the following formula to directly calculate the missing dimension of a cuboid given its surface area and two other dimensions:
x = (Total surface area - 2(bh + wh)) / 2h
Plugging in the values from the problem, we get:
x = (70 cm² - 2(3 cm * 1 cm + 3 cm * 1 cm)) / (2 * 3 cm)
x = 8 cm
So, in both ways, we arrive at the same answer: the missing length x is 8 cm.