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Three rectangular prisms each have a height of 1 cm.
Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.
Length is a one-dimensional attribute of a geometric figure. We measure lengths using units like millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles.
Area is a two-dimensional attribute. We measure area in square units. For example, a square that is 1 centimeter on each side has an area of 1 square centimeter.
Volume is a three-dimensional attribute. We measure volume in cubic units. For example, a cube that is 1 kilometer on each side has a volume of 1 cubic kilometer.
Surface area and volume are different attributes of three-dimensional figures. Surface area is a two-dimensional measure, while volume is a three-dimensional measure.
Two figures can have the same volume but different surface areas. For example:
On left, rectangular prism with side lengths of 1 centimeter, 2 centimeters, and 2 centimeters has a volume of 4 cubic centimeters and a surface area of 16 square centimeters. On right, rectangular prism with side lengths of 1 centimeter, 1 centimeter, and 4 centimeters has the same volume but a surface area of 18 square centimeters.
Similarly, two figures can have the same surface area but different volumes.
On left, rectangular prism with side lengths of 1 centimeter, 1 centimeter, and 5 centimeters has a surface area of 22 square centimeters and a volume of 5 cubic centimeters. On right, rectangular prism with side lengths of 1 centimeter, 2 centimeters, and 3 centimeters has the same surface area but a volume of 6 cubic centimeters.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.
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