Whooo hoo more math!?

Question

Hello well today (Witch was a lovely day thanks for asking) i was assigned a math problem that read like this.

heres a 1,2,3 box with no top what is the surface area? I think its 16ft2 but i could be wrong.


Then it gives me a cylinder that is radius of 1 and height of 2 what is the surface area of this? i think its 18.84 sqft


But now the big qu is how does the surface area of the 1,2,3 box compare with the surface area of the cube?

Any helpers?

A 1,2,3 box is where the dimensions are 1 by 2 by 3

Lol i mean the surface area of the cylinder haha lol i must be pretty tired sorry

Answer 1

the box is simple 2+2+3+3+(3x2)= 16 where the height is 1. using feet, meters, miles or whatever it still adds up to 16 it would be 22 if it had a top.

2x3.1416=top+bottom area add it to 2x 3.1416 x2 for side area
where 2 equals the pi rad sq twice for the areas of the top and bottom and the diameter of 2 x pi for the circumfrence (side) of one side and 2 is the height of the cylinder the other side. thus it come out to 6.2832+12.5664=18.8496 sq ft. where pi is 3.1416. the surface area of the cube is 22 while the surface area of the box is 16. of course if you also add the inside area of the box it's 32 assuming there is no depth between the inside and outside surfaces of the box if there is a cubing depth for each side you have to deduct the distance from inside and outside surfaces from the inside surface area. for example a one inch wall requires the calculations to be reduced by 1 inch of the height and 2 inches for each of the sidesthus it would be 11"x 22"x2 for the short sides and 34"x11"x2 and 34"x22". total inside area then would be (484"+748"+374")/144=11.153sq ft for inside area. add inside and outside you get 27.153 sq ft then you adds the surface area of the 1" wall on all four sides 36"+36"+10"+10" to get 92sqin wich is 92/12= 7.667 sq ft. the grand total for this would therefore be 34.82 sq ft surface area where outside and inside and one surface for the thickness of the wall are accounted for.

if you ever do this again, i'll just guess wrong to get even. it gave me a headache.

Answer 2

If the demensions of the box are 1x2x3, it still depends on where the "top of the box". is. Because the surface area is going to change depending on what side is taken away to reveal the opening. Let's assume it's the biggest, so that it's one of the 2x3 sides. That leaves the remaing four sides as two 1x2 sides and two 1x3 sides. Adding up all the areas you get 2(2*3 + 2(1*2) + 2(1+3)) = 2(6+4+8) = 2*18 = 36 square units. The reason we're multiplying the whole thing by 2 is that the surface area of an open box includes both the outside AND the inside, so we count each side twice. And again, this is assuming that the opening of the box is 2x3.

The surface area of a cylinder (assuming it's closed) is the top and bottom (which are both circles) plus the round side. This is 2pi*r*h + 2(pi*r^2), or 2pi*r(h+r). If r=1 and h=2, then the area is 2pi(1)(3) = 6pi. That's equal to 18.84 square units if you use 3.14 as the approximation for pi.

As for how the two values compare, again, it depends on how the box is being made.

Answer 3

Glad u enjoyed the day, and are delighting in extending its Mathematics component.
I think it's just asking for the ratio of surface areas. But which cube? does a 1,2,3, box mean its dimensions are 1ft by 2ft by 3ft? In that case, assuming the base is 2 by 3, I agree with you. But what are the dimensions of the cube we're supposed to be comparing it with? The cube with the same volume? Its sides would have to be the cube root of 6, which is about 1.817120593

A cube box with no top and this side length would have surface area 5*(1.817120593)^2, which is about
16.50963624, which is so surprisingly close to the other one, that I wonder if I made a mistake.

Anyway, the ratio as you can see is about 1.03185

PS I must have made a mistake. Of all rectangular prisms of a given volume, the cube is the one with least surface area. Maybe leaving the top off makes a difference. If we put the tops back on, the surface area of the cube would only go up to about 19.8 sq ft, whereas the box would go up to 22. So maybe I'm still right.

Answer 4

In a cube ,the sides are all beinbg the same,the total surface area is 6*side^2 or you may say it is 6a^2,if the sides are a unit
But in the 1,2,3 box,the lengths of the sides differ.If the length of the box be a,the breadth b and the height is c,then the total surfce area of the box will be given by the formula
2(a*b+b*c+c*a) or
2(length*breadth+length*height+breadth*height)
Total surface are of a cylinder is given by 2*Pi*r(r+h),where Pi=22/7 or 3.14 ,r is the radius of and h is the height
In this case,the total surface area would be
2*3.14*1(1+2)
=18.84
So you are 100%correct in your calculations and congratulations
for that

Answer 5

Let area of front be 2 x 1ft² = 2ft²
Area of side = 3 x 1ft² = 3ft²
Area of bottom = 2 x 3 ft² = 6ft²
Surface area = 2 x 2 + 2 x 3 + 6 ft² = 16ft²
Surface area of cylinder =2¶r² +2¶rh = 2¶r(r + h)
=2¶(1 + 2) = 6¶ = 18.84 ft²
ratio of box to cylinder = 16:18.84 = 1:1.18
Hope you agree with this!

Answer 6

First if you need help, get your unit right.
Box??? Is it a cube? if so it is 16ft3

Answer 7

what is 1,2,3 box?????