Calculate Surface Area: Finding Wrapping Paper for 20×30×70 cm Box

Ezequiel wraps a gift for his friend Dana.

The gift is a doll in whose box is packaged $20X30X70$ cm.

How many square meters of wrapping paper will Ezekiel need?

Video Solution

Solution Steps

00:00 How many square meters of paper does Yechiel need?

00:03 Let's examine the box dimensions according to the given data

00:19 Now we'll use the formula to calculate the surface area of a box

00:29 We'll substitute appropriate values and solve to find the surface area

01:06 Always solve parentheses first

01:17 This is the surface area of the box that needs to be wrapped

01:21 This is the surface area of the box in centimeters, we want to convert it to square meters

01:28 We'll divide by 100 to convert from centimeters to meters

01:43 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll proceed as follows:

Step 1: Identify the box dimensions and list them as length $l = 20 \, \text{cm}$ , width $w = 30 \, \text{cm}$ , and height $h = 70 \, \text{cm}$ .
Step 2: Use the surface area formula for a cuboid:
$A = 2(lw + lh + wh)$
Step 3: Calculate the individual areas:
- Base: $lw = 20 \times 30 = 600 \, \text{cm}^2$
- Front: $lh = 20 \times 70 = 1400 \, \text{cm}^2$
- Side: $wh = 30 \times 70 = 2100 \, \text{cm}^2$
Step 4: Compute the total surface area in cm²:
$A = 2(600 + 1400 + 2100) = 2 \times 4100 = 8200 \, \text{cm}^2$
Step 5: Convert to square meters (since $1 \, \text{m}^2 = 10,000 \, \text{cm}^2$ ):
$8200 \, \text{cm}^2 = \frac{8200}{10000} = 0.82 \, \text{m}^2$

Thus, Ezequiel needs $0.82 \, \text{m}^2$ of wrapping paper.