Question

Dayson is covering a package in the shape of a rectangular prism with wrapping paper. The package is 50 centimeters by 20 centimeters by 18 centimeters. He has 1 square meter of wrapping paper. Can he completely cover the package with wrapping paper? Complete the explanation to show your answer.

Answer 1

Yes, Dayson can completely cover the package with wrapping paper.

Explanation:

Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.

Area of wrapping paper is 1 square meter.

To find: whether he can completely cover the package with wrapping paper

Solution:

Total surface area of the rectangular prism = 2(lb + bh +hl)

where l denotes length, b denotes breadth and h denotes height

Total surface area of the rectangular prism =
`2\left [ (50)(20)+(20)(18)+(18)(50) \right ]`

`=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2`

As
`1\,m^2=10000\,cm^2`,

Total surface area of the rectangular prism =
`4520\,cm^2=0.4520\,m^2`

As Dayson has
`1\,m^2> 0.4520\,m^2` of wrapping paper, he can completely cover the package with wrapping paper.