The rectangular base of a box has a perimeter of 60cm. The base is twice as long as it is wide. Saskia plans to cover the top and bottom with coloured paper;which cost 5 cents per square centimetre. She lans to cover the other 4 faces with white paper; which costs 1.5 cents per square centimetre. How much money will Saskia spend to cover the box with paper?(assume there is no waste)
height is 40 cm .
How far have you gotten in trying to solve this problem?
i honoustly havent gotten anything done because i don't understand this at all Ms.Sue
Let the width be x
Then the length is 2x
so, 2(x+2x) = 60
6x = 60
x = 10
so, the box is 10x20
The area of the top is 10*20 = 200, as is the bottom.
There are two sides 10x40 = 2*400 = 800
and 2*20*40 = 1600
top and bottom cost 400*.05 = $20
faces cost .015*2400 = $36
Total cost: $56
thank you so much steve
To calculate the total cost of covering the box with paper, we need to find the dimensions of the base and the area of each face.
Let's start by finding the dimensions of the base:
Let X represent the width of the base in centimeters.
According to the problem, the length of the base is twice its width, so the length is 2X.
The perimeter of a rectangle can be calculated by adding up all the sides, so we have:
Perimeter = 2(length + width)
Given that the perimeter of the base is 60 cm, we can write the equation as:
60 = 2(2X + X)
Simplifying the equation:
60 = 2(3X)
Dividing both sides by 2:
30 = 3X
Dividing both sides by 3:
X = 10
So, the width of the base is 10 cm, and the length is 2 times that, which is 20 cm.
Now that we have the dimensions of the base, we can calculate the area of each face:
1. Top and bottom faces:
The area of each face is length multiplied by width, so the area of the top and bottom faces is:
Area = length * width = 20 cm * 10 cm = 200 cm^2
2. Side faces:
The height of the box is given as 40 cm, which is the same as the width of each side face. The length of each side face is the same as the length of the base, which is 20 cm.
So, the area of each side face is:
Area = length * height = 20 cm * 40 cm = 800 cm^2
Now, let's calculate the total cost of covering the box with paper:
Cost of covering the top and bottom faces:
The cost is calculated by multiplying the area by the cost per square centimeter, which is 5 cents.
Cost = Area * Cost per square cm = 200 cm^2 * 5 cents/cm^2
Cost of covering the side faces:
The cost is calculated by multiplying the area by the cost per square centimeter, which is 1.5 cents.
Cost = Area * Cost per square cm = 800 cm^2 * 1.5 cents/cm^2
Finally, let's calculate the total cost:
Total Cost = Cost of covering top and bottom faces + Cost of covering side faces
Remember to convert the cost to dollars if needed.