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