Elaine has a customer who needs a box with a volume of 12 cubic inches. The customer want to know what size box is the least expensive to buy.
.the price will be based on surface area. the supplier charges 1/2 cent persquare inch.
.the dimensions of the box are whole numbers
What size bos do you reccommend that elaine's customer buy? write a report to elaine that shows your work and explains your reccommendation.
I do not think that this is 6 grade work can someone help me with this?
Volume
cube = a^3
Surface Area
cube = 6 a^2
cubed root of 12sqin= cubed root of a
2.28942848511sqin=a
(6)2.28942848511sqin^2=31.4488962095
31.4488962095 x .5 cents=15.7244481048
6_5
Of course, I can help you with this math problem. Finding the dimensions of a box with the least expensive surface area can be done by considering all possible dimensions until we find the one with the minimum cost.
Let's start by understanding the formula for surface area and volume of a box:
Surface Area = 2lw + 2lh + 2wh
Volume = lwh
In this case, we are given the volume of the box, which is 12 cubic inches. Therefore, the equation becomes:
12 = lwh
Now, we need to find the surface area of the box using the given formula, which will help us determine the cost. The supplier charges 1/2 cent per square inch.
Cost = Surface Area * (1/2) cents
To minimize the cost, we need to minimize the surface area while keeping the volume constant. To find the least expensive size box, we need to consider all possible whole number dimensions and calculate their costs.
Here are a few sets of dimensions we can consider:
Dimensions (l, w, h) - Volume - Surface Area - Cost
1, 1, 12 - 12 - 26 - 13
1, 2, 6 - 12 - 28 - 14
1, 3, 4 - 12 - 30 - 15
2, 2, 3 - 12 - 24 - 12
2, 3, 2 - 12 - 28 - 14
3, 3, 1 - 12 - 30 - 15
4, 4, 1 - 16 - 48 - 24
6, 2, 1 - 12 - 32 - 16
By considering these dimensions and calculating their respective costs, we can see that the box with dimensions 2, 2, and 3 has the minimum cost of 12 cents. Therefore, my recommendation to Elaine's customer would be to buy a box with dimensions 2 inches by 2 inches by 3 inches.