is it possible for two boxes to have the same volume, but different surface area's? give examples to prove your point.

please help, cannot think of anything. THANKS =]

First tell me what are surfaces.

Do you mean the base?

wellit it is possible with B=0 and H=0

b is base and h is height. But i don't think having a 0 0 cube is possible! :)

Sure

Example: B-8 H-3 and B-6 H-4

Sorry, I typed thaT incorrectly...

H-8 D-1 W-1 and H-6 D-4 W-1

no for the first one the surface area would be 17? Surface area= BH+BW+WH

sure it is.

e.g.

consider a volume of 60 cm^3

box #1: 3x4x5
vol = 60
Surface area = 2(3x4 + 3x5 + 4x5) = 94

box #2: 6x2x5
volume = 60
Surface area = 2(6x2 + 6x5 + 4x5) = 124

900000000

Yes, it is indeed possible for two boxes to have the same volume but different surface areas. To understand why this is possible, consider the formula for the volume and surface area of a rectangular box:

Volume = Length x Width x Height
Surface Area = 2 x (Length x Width + Length x Height + Width x Height)

To find examples that illustrate this concept, let's start by assuming the length (L) and width (W) of both boxes are the same. We'll vary the height (H) to achieve different surface areas while keeping the volume constant.

Example 1:
Box 1: L = 4, W = 4, H = 1
Box 2: L = 4, W = 4, H = 4

In this example, both boxes have a volume of 4 x 4 x 1 = 16 cubic units. However, the surface area of Box 1 is 2 x (4 x 4 + 4 x 1 + 4 x 1) = 48 square units, while the surface area of Box 2 is 2 x (4 x 4 + 4 x 4 + 4 x 4) = 96 square units. Therefore, these boxes have the same volume but different surface areas.

Example 2:
Box 1: L = 2, W = 2, H = 8
Box 2: L = 2, W = 2, H = 1

Again, both boxes have a volume of 2 x 2 x 8 = 32 cubic units. However, the surface area of Box 1 is 2 x (2 x 2 + 2 x 8 + 2 x 8) = 64 square units, while the surface area of Box 2 is 2 x (2 x 2 + 2 x 2 + 2 x 1) = 24 square units. Thus, these boxes share the same volume but have different surface areas.

By playing around with different dimensions while maintaining the same volume, you can find numerous examples where two boxes differ in surface area while being identical in volume.