Volumes of Prisms & Cylinders

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Presentation transcript:

Volumes of Prisms & Cylinders

Volume Volume – Is the space that a figure occupies. Measured in cubic units. cm3, in3, m3, ft3

Finding the volume of a Prism Prism – 2  parallel bases and faces are rectangles. Cross sections are congruent to the bases. What is a Cross section? V = Bh Height of Prism Area of Base or Cross Section A = lw (Rectangle) Height (h) Area of Base (B)

Finding the Volume of a rectangular prism The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box?

Find the Volume of the Prism Area of Base B = l•w V = Bh = (3in • 5in)(10in) = (15in2)(10in) = 150in3 10in 3in 5in

Discussion: What prism is this. Look at the Cross Section to determine Discussion: What prism is this? Look at the Cross Section to determine. Why can’t you use l • w • h? 3 in 10in V = Bh = ½bh • h = ½(8in) __ • (10in) = (12in2) • (10in) = 120in3 8in 3in

Now work on this prism! It’s tricky so be careful. Triangle 29m V = Bh = ½bh • h = ½(20m)__ • (40m) = 210m2 • 40m = 8400m3 a 40m 21 20m Height of the base: a2 + b2 = c2 a2 + 202 = 292 a = 21

Volume of a Cylinder Video for help: YouTube Height of cylinder r V = Bh h Volume of right cylinder Area of base or cross section: (Circle) A = r2

Ex.4: Find the area of the following right cylinder. Area of a Circle V = Bh = r2 • h = 3.14(8ft)2 • (9ft) = 200.96ft2 • (9ft) = 1809.6ft3 16ft 9ft

Ex.5: Find the volume of the following composite figure. Half of a cylinder: Vc = Bh = r2•h = (6in)2 • (4in) = 452in3 = 452/2 = 226in3 11in 4in Volume of Prism: Vp = Bh = (11)(12)(4) = 528in3 12in VT = Vc + Vp = 226in3 + 528in3 = 754in3

What have we learned?? Volume of a prism or a cylinder: V = Bh Capitol “B” stands for area of the base. Composite Figures: Made up of two separate solids.