The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is 4 ft high and has a total surface area of 220 ft^2. Which equation can you use to solve this problem?
4w^2 + 8w = 220
4w^2 –16w = 220
4w^2 + 24w = 220
4w^2 –24w = 220
2007-12-16 13:43:26 · 5 answers · asked by Lola L 1 in Science & Mathematics ➔ Mathematics
^means that the number next to it is an exponent
example
3 squared = 3^2
2007-12-16 13:51:18 · update #1
L = 2w, so area of top and bottom is 2(Lw) = 2(2w²) = 4w². area of long sides is 2(4L) = 8L = 16w, and area of short sides is 2(4w) = 8w, so total surface area is
4w² + 24w = 220
w² + 6w - 55 = 0
(w+11)(w-5) = 0
w = 5, L = 10, so
volume = 5(10)(4) = 200 ft.³
2007-12-16 13:52:21 · answer #1 · answered by Philo 7 · 1⤊ 0⤋
The third one. total surface area is the sum of the area of all the sides. there are two sided that are 2w x 4. so that gives you 16 w. there are two sides that are w x 4 so that is 8 w. total of 24 w. then the top and bottom area is 2w x w = 2w^2. two of those means 4w^2. So you can find the width by using 4w^2 + 24w = 220
2007-12-16 21:58:39 · answer #2 · answered by michael c 3 · 0⤊ 0⤋
4w^2 + 8w = 220
The top and bottom of the box is 2w (twice as long as it is wide) and each side of the box is w. Add them up to find the surface area, which is equal to 220, and you'll get the equation above.
2007-12-16 21:58:31 · answer #3 · answered by dazed and confused 2 · 0⤊ 1⤋
Let's do it step by step.
top and bottom are rectangles. area of a rectangle is a * b.
but in our rectangles a - width , 2a - length;
our area: a * 2a = 2a^2
The height of the box is 4.
he box is then a cuboid, where height is 4 and base and top are rectangles with the area of 2a^2.
We know the surface area:
top + bottom + four sides.( 2 + 2)
What is the area of left and right side? this sides have following lengths: a form the base and 4 from the height.
Area: 4a (2 sides 8a)
front and back: 2a from the base and 4 from the height.
Area: 2a*4 = 8a (2 sides 16a)
Now total surface area:
base*2 + front + back + left + right =
= 4a^2 + 8a + 16a = 4a^2 + 24a
we know that SA = 220
therefore: 4a^2 + 24a = 220
answer 3 then. I simply used different notation (a = w)
Good Luck
2007-12-16 21:55:30 · answer #4 · answered by Anonymous · 1⤊ 0⤋
If you let me know what ^ means, I'll solve it for you.
2007-12-16 21:48:59 · answer #5 · answered by Mystikdancer 3 · 0⤊ 3⤋