Volume a nd Surface Area

Volume and Surface Area

Volume is the area of the base times the height… h is height 1 unit 1 unit 1 unit w is width l is length V = (lw)h V = 4(3)(5) V = 60 cubic units

Note the same for a cylinder… r = 3 units 1 unit Remember the base of a cylinder is a circle. V = (r2)h V = π(9)(4) V  113 units cubed

Example #1 r = 5 cm r = 10 cm h = 6 cm h = 6 cm Two cylinders have the same height, but the radius of the second is twice that of the first. What is the ratio of the first cylinder to the second as a simplified fraction?

You have been given two nets. Cut these out and fold on the dotted lines. What figures do these create? Cylinder Rectangular Prism

Example #2 Use your ruler to calculate the volume of each of these solids. length is 6 mm Width is 3 mm Height is 1.5 mm

Example 2 continued… Height is 2.7 mm Length is 12.6 mm Radius is 2mm

Example #3 Surface area is the total area of the outside of a figure. A net is a good way to visualize the shapes of the surfaces of a solid. Let’s find the area of both of these nets. What formulas will you need for this task? Area formula for a rectangle…A = lw Area formula for circle…A = πr2 You can also remember these… SA = 2lw + 2lh + 2wh SA = 2πr2+ πDh

Example #3 Height is 2.7 mm Length is 12.6 mm (This is the circumference) Radius is 2mm

Example #3 continued… 9 mm2 length is 6 mm 4.5 mm2 A = wh A = 3(1.5) A = 4.5 mm2 A = lw A = (6)(3) A = 18 mm2 Width is 3 mm 18 mm2 A = lh A = (6)(1.5) A = 9 mm2 Height is 1.5 mm

Volume a nd Surface Area