A box has a square bottom and top and is 5cm high. Find its volume if its total surface area is 192cm squared

Question

PLEASE i need to know how to do it not just the answer

Answer 1

Define what they tell you

Volume = area of aquare * height = x^2 * 5 = 5x^2

Surface area = surface areas of all the sides
Two sides have square areas and the other four sides have rectangular areas:
SA = x^2 + x^2 + 5x + 5x + 5x + 5x = 192
2x^2 +20x = 192
2x^2 +20x - 192 = 0
x^2 +10x - 96 = 0
(x + 16)(x - 6) = 0
x = 6 or -16
Pick x = 6 cm, since length is positive..

Now use x = 6cm in the volume equation

V = 5(6 cm)^2 = 30 cm^2

Answer 2

The first answer is wrong.

[it helps if you draw a picture] The box has six faces. The total surface area of the faces is 192 cm squared. How do you calculate the surface area of the box? Add up the area of each quadrilateral that makes up each face.

What is the surface area of the top? It's a square. We don't know the lenght/width but they are the same. Let's call each side "a" so the area of the top is a^2 (squared). The "bottom" is opposite of the top and has the exact same area. So the top and bottom are 2a^2.

What is the surface area of the side? It's a quadrilateral. We know one dimension is 5 cm because we were told that and the other dimension is what we called "a" because the sides share that with top and bottom faces. So the area of a side is 5a. You can see that each side face is exactly the same dimensions so you have 4 of them so the total is 20a.

So the total surface area is 2a^2 + 20a = 192. Solve for a. [it's been so long since i did high school algebra I can't remember how to do this without plugging in values] You can see the answer that solves a is 6.

So now the volume is trivial because the volume of a box is height * length * width. So 5 * 6 * 6 = or 180 cubic cm.

Answer 3

Let the side of the square be x cm. Hence the total surface area would be: 2x^2 (base plus top) + 4*5*x (four vertical sides, since height is 5 cm) i.e. 2x^2+20x sq. cms. which is stated to be 192. Hence 2x^2 + 20x =192 or x^2+10x-96=0. Solving, (x+16)(x-6)=0. Since x is a positive number, the value required is 6 cm.
Volume is area of base* height or 6*6*5=180 cubic cms.

Answer 4

total surface area=4(5)(length or L) + 2(length squared)
192=4(5)(L)+2L squared
192=20L+2L squared
divide the equation by 2 t reduce the values so you have:
96=10L+2L squared then factor it out so yu have:
(L+16)(L-6).hence the values for L are -16 and 6.since you are looking for a value of measurement,choose the positive value which is 6.
volume=LxWxH but L=W
V=6x6x5
V=180cm cube

Answer 5

l * w* 5 cm=192 cm^2
l*w=38.4

find the square root of 38.4 cm^2

that will be the answer for l and w