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
= 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
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
Where u is the pore water pressure (p.w.p.) Then Eq. (9) becomes . ??=?′+(?? −?) ??? ∅′ ….(??) C , or C ', ' are called . strength parameters, and we will discuss various laboratory tests for their determination. But...
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