Draw two different composite solids that have the same volume but different surface areas. Explain your reasoning.

Two different solids are shown in figure.

1) A cube of side, 4 cm.

Volume of cube = side * side * side = 4*4*4 = 64 cm cubic centimeters

Surface area of cube = 6 * side * side = 6 * 4*4 = 96 cm^2

2) A rectangular prism of dimensions, l = 8cm, h = 4 cm and b = 2 cm

Volume of rectangular prism = side * side * side = 8*4*2 = 64 cm cubic centimeters

Surface area of rectangular prism = 2lb + 2bh + 2hl

= 2*4*8 + 2*8*2 + 2*2*4

= 112 cm^2

The volume of both these solids are same but the surface area is different because volume means holding/containing something while surface area depends on the area of each surface in the figure. The surfaces in the cube are squares but in rectangular prism, the surfaces are rectangles.