Finding Volume and Surface Area

Show What You Know What is volume? 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

Show What You Know What formula would I use to find the volume of a rectangular prism? a b c (a+b) * c a+b+c abc I don’t know

Show What You Know What formula would I use to find the volume of a cylinder? (2πr) * h I don’t know (πr 2 ) * h (πd) * h

Show What You Know What is surface area? 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

Show What You Know What formula would I use to find the surface area of a rectangular prism? a b c 2ab+2ac+2bc a+b+c abc I don’t know

Show What You Know What formula would I use to find the surface area of a cylinder? (2πr) * h I don’t know 2(πr 2 ) + h(πd) (πd) * h

Volume  Volume is a measure of what it would take to fill a figure in units cubed (ex. in 3, ft 3, etc.)  For cylinders and prisms, it is found by multiplying the area of the base of a figure times its height  Try this activity Try this activity Try this activity  Click here to try the next question! Click here to try the next question! Click here to try the next question!

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Finding Volume  To find the volume of a prism, multiply the area of the base by the height. 3 in 2 in 5 in Area of the base = 2 * 3 = 6 in 2 Volume = area of the base * height 6 in 2 * 5 in = 30 in 3 next

Finding Volume Cont’d  For a triangular prism, find the area of the base x height  Area of base = ½ * 2 * 2 = 2 ft 2  Area of base x height = 2 ft 2 * 4 ft  Volume = 8 ft 3 2 ft 4 ft For any prism, multiply the area of the base by the height.prism  Click here to try the next question! Click here to try the next question! Click here to try the next question!

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Cylinders and Volume  To find the volume of a cylinder, multiply the area of the base by the height  Area of a circle = πr 2 (Pie Are Square)  Area of a circle = πr 2 (Pie Are Square) 4 cm 2 cm πr2 = 3.14 * 4 2 = cm cm 2 * 2 cm = cm cm 2 * 2 cm = cm 3  Click here to try the next question! Click here to try the next question! Click here to try the next question!

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Surface Area  Surface area is what it would take to wrap a 3D shape.  It is equal to the sum of the area of all surfaces in the shape a 2 in 1 in 3 in b c There are 6 faces in all 2 faces are the same as face a (2 x 1) 2 faces are the same as face b (3 x 1) 2 faces are the same as face c (3 x 2) So, 2(2x1) + 2(3x1) + 2(3x2) = 18 in 2 See how volume and surface area change when the dimensions are changed!  Click here to try the next question! Click here to try the next question! Click here to try the next question!

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Surface Area  Surface area is what it would take to wrap a 3D shape.  It is equal to the sum of the area of all surfaces in the shape a 2 in 1 in 3 in b c There are 6 faces in all 2 faces are the same as face a (2 x 1) 2 faces are the same as face b (3 x 1) 2 faces are the same as face c (3 x 2) So, 2(2x1) + 2(3x1) + 2(3x2) = 18 in 2 See how volume and surface area change when the dimensions are changed!  Click here to try the next question! Click here to try the next question! Click here to try the next question!

Great Work!  Now try some problems of your own!  Print and complete the following worksheet (select worksheet #3) on finding volume Print and complete the following worksheet (select worksheet #3) on finding volume Print and complete the following worksheet (select worksheet #3) on finding volume  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. portaportal.com

Surface Area and Cylinders  A cylinder is made up of 3 surfaces- two circles and a rectangle The area of the circle is πr 2. Since you have 2 circles, you will use 2(πr 2 ). 2(3.14 x 1 2 ) = 6.28 cm 2 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 * 2πr (or πd). 4 * 2(3.14*1) = 4 * 6.28 = cm 2 Together, you have = 31.4 cm 2 1 cm 4 cm next