Surface Area Calculation: Find Total Area of 5 dm × 4 cm × 0.3 dm Box

Question

Calculate the surface area of the box shown in the diagram.

Pay attention to the units of measure!

5 dm5 dm5 dm4 cm4 cm4 cm0.3 dm0.3 dm0.3 dm

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert all dimensions to the same unit.

  • Step 2: Apply the surface area formula for a cuboid.

  • Step 3: Calculate the total surface area.

Now, let's work through each step:

Step 1: Convert all dimensions to the same unit. For consistency, we will convert everything to decimeters (dm):

  • Width = 5 dm (already in dm)

  • Height = 4 cm. To convert cm to dm, divide by 10: 4cm=0.4dm 4 \, \text{cm} = 0.4 \, \text{dm} .

  • Depth = 0.3 dm (already in dm)

Step 2: Apply the surface area formula for a cuboid:

The surface area A A is given by:

A=2lw+2lh+2wh A = 2lw + 2lh + 2wh

Where:

  • l=0.3dm l = 0.3 \, \text{dm} (depth)

  • w=5dm w = 5 \, \text{dm} (width)

  • h=0.4dm h = 0.4 \, \text{dm} (height converted to dm)

Substitute these values into the formula:

A=2(0.3)(5)+2(0.3)(0.4)+2(5)(0.4) A = 2(0.3)(5) + 2(0.3)(0.4) + 2(5)(0.4)

Step 3: Calculate the surface area:

A=2(1.5)+2(0.12)+2(2) A = 2(1.5) + 2(0.12) + 2(2)

A=3+0.24+4 A = 3 + 0.24 + 4

A=7.24dm2 A = 7.24 \, \text{dm}^2

Note that the question requires the surface area in different units.

Thus, 7.24 dm² is 72.4 cm²

Therefore, the solution to the problem is 72.4 cm².

Answer

72.4 cm²