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Transcript of "3D Figures- volume and surface area"
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Finding Volume and Surface Area 3D Figures
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Show What You Know <ul><li>What is volume? </li></ul>A measure of what is needed to cover a 3D shape A measure of what is needed to fill a 3D shape A measure of the inside surfaces of a 3D shape I don’t know
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Show What You Know <ul><li>What formula would I use to find the volume of a rectangular prism? </li></ul>a b c (a+b) * c a+b+c abc I don’t know
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Show What You Know <ul><li>What formula would I use to find the volume of a cylinder? </li></ul>(2 π r ) * h I don’t know ( π r 2 ) * h ( π d ) * h
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Show What You Know <ul><li>What is surface area? </li></ul>A measure of what is needed to cover a 3D shape A measure of what is needed to fill a 3D shape A measure of the area of the base of a 3D shape I don’t know
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Show What You Know <ul><li>What formula would I use to find the surface area of a rectangular prism? </li></ul>a b c 2ab+2ac+2bc a+b+c abc I don’t know
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Show What You Know <ul><li>What formula would I use to find the surface area of a cylinder? </li></ul>(2 π r ) * h I don’t know 2( π r 2 ) + h( π d) ( π d ) * h
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Volume <ul><li>Volume is a measure of what it would take to fill a figure in units cubed (ex. in 3 , ft 3 , etc.) </li></ul><ul><li>For cylinders and prisms, it is found by multiplying the area of the base of a figure times its height </li></ul><ul><li>Try this activity </li></ul><ul><li>Click here to try the next question! </li></ul>
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Great Work! <ul><li>Click here to try the next question! </li></ul>
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Awesome! <ul><li>Click here to try the next question! </li></ul>
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Finding Volume <ul><li>To find the volume of a prism, multiply the area of the base by the height. </li></ul>3 in 2 in 5 in <ul><li>Area of the base = 2 * 3 = 6 in 2 </li></ul><ul><li>Volume = area of the base * height </li></ul><ul><li>6 in 2 * 5 in = 30 in 3 </li></ul>next
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Finding Volume Cont’d <ul><li>For a triangular prism, find the area of the base x height </li></ul><ul><li>Area of base = ½ * 2 * 2 = 2 ft 2 </li></ul><ul><li>Area of base x height = 2 ft 2 * 4 ft </li></ul><ul><li>Volume = 8 ft 3 </li></ul>2 ft 2 ft 4 ft For any prism , multiply the area of the base by the height. <ul><li>Click here to try the next question! </li></ul>
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Excellent! <ul><li>Click here to try the next question! </li></ul>
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Cylinders and Volume <ul><li>To find the volume of a cylinder, multiply the area of the base by the height </li></ul><ul><li>Area of a circle = π r 2 (Pie Are Square) </li></ul>4 cm 2 cm <ul><li>π r2 = 3.14 * 4 2 = 50.24 cm2 </li></ul><ul><li>50.24 cm 2 * 2 cm = 100.48 cm 3 </li></ul><ul><li>Click here to try the next question! </li></ul>
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Way to go! <ul><li>Click here to try the next question! </li></ul>
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Surface Area <ul><li>Surface area is what it would take to wrap a 3D shape. </li></ul><ul><li>It is equal to the sum of the area of all surfaces in the shape </li></ul>a 2 in 1 in 3 in b c <ul><li>There are 6 faces in all </li></ul><ul><li>2 faces are the same as face a (2 x 1) </li></ul><ul><li>2 faces are the same as face b (3 x 1) </li></ul><ul><li>2 faces are the same as face c (3 x 2) </li></ul><ul><li>So, 2(2x1) + 2(3x1) + 2(3x2) = 18 in 2 </li></ul>See how volume and surface area change when the dimensions are changed! <ul><li>Click here to try the next question! </li></ul>
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You’ve Got It! <ul><li>Click here to try the next question! </li></ul>
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Surface Area <ul><li>Surface area is what it would take to wrap a 3D shape. </li></ul><ul><li>It is equal to the sum of the area of all surfaces in the shape </li></ul>a 2 in 1 in 3 in b c <ul><li>There are 6 faces in all </li></ul><ul><li>2 faces are the same as face a (2 x 1) </li></ul><ul><li>2 faces are the same as face b (3 x 1) </li></ul><ul><li>2 faces are the same as face c (3 x 2) </li></ul><ul><li>So, 2(2x1) + 2(3x1) + 2(3x2) = 18 in 2 </li></ul>See how volume and surface area change when the dimensions are changed! <ul><li>Click here to try the next question! </li></ul>
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Great Work! <ul><li>Now try some problems of your own! </li></ul><ul><li>Print and complete the following worksheet (select worksheet #3) on finding volume </li></ul><ul><li>Try some of the websites on portaportal.com in the geometry section on volume and surface area. You may also look at some of the sites on 3D shapes. </li></ul>
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Surface Area and Cylinders <ul><li>A cylinder is made up of 3 surfaces- two circles and a rectangle </li></ul><ul><li>The area of the circle is π r 2 . Since you have 2 circles, you will use 2( π r 2 ). 2(3.14 x 1 2 ) = 6.28 cm 2 </li></ul><ul><li>The rectangle has one side = to the height of your cylinder, and one side = to the circumference of your circle. So, you will use height * 2 π r (or π d). 4 * 2(3.14*1) = 4 * 6.28 = 25.12 cm 2 </li></ul><ul><li>Together, you have 6.28 + 25.12 = 31.4 cm 2 </li></ul>1 cm 4 cm next
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