Question

Stacy is covering the box below with sticky wrapping paper. If the paper cost 2 cents per square centimeter, how much will it cost to cover the entire box.

Answer 1

Given:

The shape of box is a right triangular prism.

Paper cost = 2 cents per square centimeter

To find:

The cost to cover the entire box.

Solution:

In the given right triangular prism, we have 3 rectangle surfaces and 2 triangular surfaces.

Area of a rectangle is

`Area=length* width`

Area of rectangle with length 4 cm and width 3 cm is

`A_1=4* 3=12\text{ cm}^2`

Area of rectangle with length 4 cm and width 4 cm is

`A_2=4* 4=16\text{ cm}^2`

Area of rectangle with length 4 cm and width 5 cm is

`A_3=4* 5=20\text{ cm}^2`

Area of a triangle is

`Area=(1)/(2)* base* height`

Area of triangle with base 3 cm and height 4 cm is

`A_4=(1)/(2)* 3* 4`

`A_4=(12)/(2)`

`A_4=6\text{ cm}^2`

Bottom and top triangular surfaces are equal.

`A_5=A_4=6\text{ cm}^2`

Now, total surface area of the box is

`A=A_1+A_2+A_3+A_4+A_5`

`A=12+16+20+6+6`

`A=60\text{ cm}^2`

Paper cost = 2 cents per square centimeter

Cost of 60 square centimeter paper is

`60* 2=120\text{ cents}`

Therefore, the cost to cover the entire box is 120 cents or $1.2.