word problem

Question

Oscar is giving his mother a new acquarium in the shape of a rectuangular prism. He is going to wrap it in colorful wrapping paper. He know that he needs exactly 2,948 square inches of paper to wrap the aquarium. If the acuqarium is 40 inches long and 18 inches wide, what is the height of the aquariaum? 
a) 13 inches 
b) 14 inches 
c) 15 inches 
d) 16 inches

Answer 1

Any 3-dimensional box, such as the aquarium in the question, has 6 sides. If we calculate the area of each side, we know that the total surface area of the box is 2948 in. Let's come up with expressions for the area for each of the six sides:

 

There are two "large" sides - the front and back, which each have an area equal to length x height

 

There are two "small" sides - the left and right sides, which each have an area equal to width x height

 

Finally, there is a top and a bottom, which each have an area equal to length x width.

 

We can write an equation for the total surface area:

 

2*(l*h) + 2*(w*h) + 2*(l*w) = 2948

 

We have values for length and width, so we can plug them into the equation, and rearrange to solve for height:

 

2*(40*h) + 2*(18*h) + 2*(40*18) = 2948

 

80*h + 36*h + 1440 = 2948

 

116*h +1440 = 2948

 

116*h = 1508

 

h = 13

Answer 2

Well, we know that the formula to find the surface area  of a rectangle is A = 2(wh + lw + lh).

We plug in what we know.

 

SA (surface area) = 2948 in^2

l = 40 in

w = 18 in

h = ?

 

2948 = 2(18h + (40*18) +40h) (Multiply 40 and 18 and add the like terms)

 

2948 = 2(58h +720)  (Multiply the right side by 2 using the distributive property)

 

2948 = (2*58h) + (2*720)

 

2948 = 116h + 1440 (Subtract 1440 from both sides)

 

2948 - 1440 = 116h + 1440 - 1440

 

1508 = 116h (divide both sides by 116 to find h)

 

1508/116 = 116h/116

 

13 = h

 

Therefore, the height of your aquarium is 13 inches.

 

Answer 3

Surface area of a rectangular prism includes 6 sides, 3 pairs of 2 opposing sides that have equal areas.

 

2 have areas of l*w, 2 have areas of w*h, and 2 have areas of l*h.

 

2lw + 2wh + 2lh = 2948

 

2(40)(18) + 2(18)h + 2(40)h = 2948

 

1440 + 36h + 80h = 2948

 

1440 + 116h = 2948

-1440               -1440

 

116h = 1508

 

Divide both by 116...

 

h = 1508/116 = 13 inches.

 

a) is the correct answer.

 

 

Answer 4

Hi Andrea;

The aquarium has six sides, like any other box.

sides....2(width)(length)

sides...2(height)(length)

sides...2(height)(width)

 

We have the area, length and width, we need the height:  2948 in² area, 40 in long and 18 in wide.

 

x=height

 

Our first priority is to verify that all units match.  For example, one dimension may have been provided in feet or yardage.  But everything is in inches.  So no further action is required on that issue.

 

2,948=2(w)(l)+2(h)(l)+2(h)(w)

We can save some work by dividing both sides by 2...

2948/2=[2(w)(l)+2(h)(l)+2(h)(w)]/2

1474=(w)(l)+(h)(l)+(h)(w)

1474=(18)(40)+(h)(40)+(h)(18)

1474=720+h(40+18)

Let's subtract 720 from both sides as we proceed to isolate h...

1474-720=-720+720+h(58)

754=h(58)

Let's divide both sides by 58

754/58=h(58)/58

13=h=height

 

The answer is (a)