# Volume of Prisms, Pyramids, Cylinders and Cones Volume of Prisms, Pyramids, Cylinders and Cones LEARNING TARGET: I can explain the difference between the volume of pyramids, cones, and prisms and cylinders. I. Finding the volume of a Prism V = Bh V = lwh Area of the base (rectangular) Height (h) V= ( bh) h

(triangular) Area of Base (B) Height of triangle Height of prism Ex.1: Find the Volume of the Prism V = Bh and rectangular so V = lwh 10in 5in = (3in 5in)(10in)

= (15in2)(10in) 3in = 150in3 Ex.2: Find the volume of the following prism. Triangle 29m V = Bh a = bh h 40m a +b =c

2 20m Height of the base: 2 2 = (20m)__ 21 (40m) a2 + 202 = 292 = 210m2 40m a2 + 400 = 841

= 8400m3 a2 = 441 b = 21 Ex.3: Yet another prism! Find the volume. 8 10in 8in h 4 V = Bh

a2 + b2 = c2 = bh h 42 + h2 = 82 = (8in) 6.9 __ (10in) 16 + h2 = 64 = (27.7in2) (10in) = 277in3 h2 = 48 h = 6.9 II. Volume of a Cylinder

r V = Bh h V=rh 2 Ex.4: Find the volume of the following cylinder. V = Bh = r2 h 16ft = (8ft)2 (9ft) 9ft

= 64ft2 (9ft) = 576ft3 = 1809.6ft3 What have we learned??? Volume of Prisms & Cylinders r V = (area of base) h h 10in 5in 3in I. Volume of a Pyramid Vp = (area of base) h

Area of the Base A = lw bh A= Height of the pyramid, not to be confused with the slant height (l) h Ex.1: Volume of a right Pyramid Find the volume of a square pyramid with base edges of 15cm & a height of 22cm. Square

V = (area of base)h = ()bbh 22cm 15cm 15cm = ()151522 = ()4950 = 1650cm3 Ex.2: Another square pyramid Find the area of a square pyramid w/ base edges 16ft long & a slant height 17ft. V = ()Bh a +b =c

h2 + 82 = 172 h2 + 64 = 289 h2 = 225 h = 15 2 2 = ()lwh 2 h 17ft 8ft

16ft = ()1616___ 15 = ()3840 16ft = 1280ft3 II. Volume of a Cone 2 Vc = r h Area of the Base h

r Height of the cone, not to be confused with the slant height (l) Ex.3: Find the volume of the following right cone w/ a diameter of 6in. Circle 11in 3in V = r2h = () (3)2(11) = ()99 = 33 = 103.7in3

Ex.5: Solve for the missing variable. The following cone has a volume of 110. What is its radius. V = (r2)h 110 = ()r2(10) 110 = ()r2(10) 10cm 11 = ()r2 33 = r2 r r = (33) = 5.7cm What have we learned??? Volume of Cones & Pyramids V = (area of base)h

h h r