LER 7630 TM ACTIVITY GUIDE A Hands-on Approach to Learning About Area and Volume
Hemisphere Cylinder Cone Sphere Triangular Pyramid Square Pyramid Small Triangular Prism Large Triangular Prism Hexagonal Prism Large Rectangular Prism Small Rectangular Prism Large Square Prism V = 1/2 x (4/3 π x r3) V=Ax H V = 1/3 A x H V = 4/3 π x r3 V = 1/3 A x H V = 1/3 A x H V=AxH V=AxH V=AxH V=Ax H V=Ax H V=Ax H V = 1/2 x (4/3 π x r3) V = (π x r2) x H V = 1/3(π x r2) x H V = 4/3 π x r3 V = 1/3 (1/2 x b x h) x H V = 1/3 (1 x w) x H V = (1/2 x b x h) x H V = (1/2 x b x
Introduction The transparent Power Solids™ set includes 12 plastic three-dimensional shapes that allow for hands-on study of volume. Power Solids can be integrated easily with daily math lessons for introducing, teaching, and reviewing math concepts effectively. They allow students to make concrete connections between geometric shapes and their associated formulas for volume, and to observe volumetric relationships between the geometric shapes as well.
Ask students how they might organize the shapes into categories based on their features. Write students’ answers on the board. Then, define pyramids and prisms. Hold up an example of a prism and a pyramid for the class. Encourage students to organize the Power Solids again based on this information. Discuss and explain the cylinder, sphere, and cone as exceptions. Work with students to create a table like this one to record their observations.
Introducing Volume Volume, or the capacity of an object, is sometimes confused with surface area. At first glance, the formulas appear somewhat similar. A helpful way to compare the concepts is to explain surface area as the amount of room on the outside of a shape, and volume as the amount of space inside a shape. Discuss the value of measuring volume, giving such examples as knowing how much water a pool will hold, how much air a SCUBA tank will hold, or how much cement a cement mixer will hold.
Volume Formulas Prism Finding the volume of a general prism is a matter of multiplying the area of the base times the height of the prism: Volumegeneral prism = A x H Identify the variables: A = Area of the base H = Height of the prism The formula for the area of the base of the prism depends upon the shape of the base.
H Hexagonal Prism Volumehexagonal prism = A x H Identify the variables: A = Area of the hexagonal base H = Height of the prism Explain that the area for a hexagon is calculated as follows: A = w x 3 /2 s w Identify the variables: w = Width of hexagon as shown s = Length of side s r Cylinder Volumecylinder = A x H = (π r2) x H H Pyramid Introduce the general formula for finding the volume of a pyramid: Volumepyramid = 1/3 A x H Ask students to identify the difference between this general formula an
b Triangular Pyramid Volumetriangular pyramid = 1/3 A x H = 1/3 (b x h) x H Cone Volumecone = 1/3 A x H = 1/3 (π r2) x H H h H r r Sphere Volumesphere = 4/3 π r2 Also from Learning Resources®: • LER 7631 Investigating with Power Solids™ • LER 7633 Geometry Template Visit our web site at: © Learning Resources, Inc., Vernon Hills, IL (U.S.A.) Learning Resources Ltd., King’s Lynn, Norfolk (U.K.) Please retain our address for future reference. Made in China.
