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 .
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To figure out how much money Saskia will spend to cover the box with paper, we need to find the surface area of the box and then calculate the cost based on the cost per square centimeter.
Let's start by finding the dimensions of the rectangular base.
Let the width be "w" cm.
According to the given information, the length of the base is twice as long as the width, so the length is 2w cm.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, the perimeter is given as 60 cm, so we can write the equation:
60 = 2(2w + w)
Simplifying the equation:
60 = 2(3w)
30 = 3w
w = 10 cm
So, the width of the rectangle is 10 cm and the length is twice the width, which is 20 cm.
Now, let's calculate the surface area.
The top and bottom surfaces are rectangular and have the same dimensions as the base, so the area of each surface is: length x width = 20 cm x 10 cm = 200 cm^2
The other four faces are rectangular as well, but they have different dimensions.
The height of the box is given as 40 cm, so the dimensions of the four side faces are:
Length = 40 cm
Width = 20 cm
The area of each side face is: length x width = 40 cm x 20 cm = 800 cm^2
Now, let's calculate the total surface area of the box.
Total Surface Area = 2(top and bottom) + 4(side faces)
Total Surface Area = 2(200 cm^2) + 4(800 cm^2)
Total Surface Area = 200 cm^2 + 3200 cm^2
Total Surface Area = 3400 cm^2
Next, we calculate the cost of covering the top and bottom surfaces with colored paper (5 cents per square centimeter).
Cost of Colored Paper = Area x Cost per cm^2
Cost of Colored Paper = 2(200 cm^2) x 5 cents/cm^2
Cost of Colored Paper = 400 cm^2 x 5 cents/cm^2
Cost of Colored Paper = 2000 cents
Next, we calculate the cost of covering the other four faces with white paper (1.5 cents per square centimeter).
Cost of White Paper = Area x Cost per cm^2
Cost of White Paper = 4(800 cm^2) x 1.5 cents/cm^2
Cost of White Paper = 3200 cm^2 x 1.5 cents/cm^2
Cost of White Paper = 4800 cents
Finally, let's calculate the total cost of covering the box with paper.
Total Cost = Cost of Colored Paper + Cost of White Paper
Total Cost = 2000 cents + 4800 cents
Total Cost = 6800 cents
So Saskia will spend 6800 cents (or $68) to cover the box with paper.