Question
Wooden door stopper needs to be covered with stickers to match the door for a directing contest. If one package of stickers covers a surface area of 75 cm², how many packages of stickers needed to be purchased? (find the closest number to the surface area of the door stopper. Stickers may only be purchased in whole packs.) they dimensions are 15.9 cm, 8.9 cm, 5 cm and 16.7 cm
Answers
GPT-4o mini
To determine how many packages of stickers are needed to cover the surface area of the wooden door stopper, we first need to calculate the total surface area of the door stopper.
The wooden door stopper is likely a rectangular prism, so we can find the surface area using the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the length, width, and height of the stopper, respectively.
Let's assume the dimensions you provided are:
- Length (\( l \)) = 15.9 cm
- Width (\( w \)) = 8.9 cm
- Height (\( h \)) = 5 cm
Calculating the surface area:
1. Find the area of each pair of opposite faces:
- \( lw = 15.9 \times 8.9 \)
- \( lh = 15.9 \times 5 \)
- \( wh = 8.9 \times 5 \)
2. Now calculate each area:
- \( lw = 15.9 \times 8.9 = 141.51 \, \text{cm}^2 \)
- \( lh = 15.9 \times 5 = 79.5 \, \text{cm}^2 \)
- \( wh = 8.9 \times 5 = 44.5 \, \text{cm}^2 \)
3. Calculate the total surface area:
\[
\text{Surface Area} = 2(lw + lh + wh) = 2(141.51 + 79.5 + 44.5)
\]
\[
= 2(265.51) = 531.02 \, \text{cm}^2
\]
Now, we need to find how many packages of stickers are needed. Each package covers 75 cm².
To find the number of packages required, divide the total surface area by the coverage per package:
\[
\text{Number of packages} = \frac{\text{Surface Area}}{\text{Coverage per package}} = \frac{531.02}{75} \approx 7.08
\]
Since stickers can only be purchased in whole packages, we round up to the next whole number:
\[
\text{Packages needed} = 8
\]
Therefore, **you will need to purchase 8 packages of stickers** to cover the wooden door stopper.
The wooden door stopper is likely a rectangular prism, so we can find the surface area using the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the length, width, and height of the stopper, respectively.
Let's assume the dimensions you provided are:
- Length (\( l \)) = 15.9 cm
- Width (\( w \)) = 8.9 cm
- Height (\( h \)) = 5 cm
Calculating the surface area:
1. Find the area of each pair of opposite faces:
- \( lw = 15.9 \times 8.9 \)
- \( lh = 15.9 \times 5 \)
- \( wh = 8.9 \times 5 \)
2. Now calculate each area:
- \( lw = 15.9 \times 8.9 = 141.51 \, \text{cm}^2 \)
- \( lh = 15.9 \times 5 = 79.5 \, \text{cm}^2 \)
- \( wh = 8.9 \times 5 = 44.5 \, \text{cm}^2 \)
3. Calculate the total surface area:
\[
\text{Surface Area} = 2(lw + lh + wh) = 2(141.51 + 79.5 + 44.5)
\]
\[
= 2(265.51) = 531.02 \, \text{cm}^2
\]
Now, we need to find how many packages of stickers are needed. Each package covers 75 cm².
To find the number of packages required, divide the total surface area by the coverage per package:
\[
\text{Number of packages} = \frac{\text{Surface Area}}{\text{Coverage per package}} = \frac{531.02}{75} \approx 7.08
\]
Since stickers can only be purchased in whole packages, we round up to the next whole number:
\[
\text{Packages needed} = 8
\]
Therefore, **you will need to purchase 8 packages of stickers** to cover the wooden door stopper.