# 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

## Recently Viewed Presentations

• 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...
• Pedra da Gávea vista de onde hoje é favela da Rocinha Palácio Guanabara visto da Rua Paissandu, no Flamengo Biblioteca, mapoteca, arquivo e lago do Palácio Itamaraty O "Graff Zeppellin" sobre a enseada de Botafogo O Centro da cidade visto...
• Committal and actions. Prayer over the place of committal. Committal. Prayer. Intercessions. The Lord's Prayer. Concluding Prayer. Prayer over the people. Two groups: How would you lead these Rites? Gathering in the Presence of the body . Pat. Academy Room....
• The Eco-Approach and Departure at Signalized Intersections application was selected to test its efficacy and usefulness. ... (SPaT) and Geographic Information Description (GID) messages using vehicle-to-infrastructure (V2I) communications .
• In the Sumerian myth, "Enki and the World Order," Enki is said to have fixed national boundaries and assigned gods their roles. According to another Sumerian myth Enki is the creator, having devised men as slaves to the gods. In...
• • Requires two sets of everything (staff, equipment, etc.). • Requires software to control changeover (e.g., do not mail two sets of payments). • Requires automated scripts to compare results. Parallel testing may take several months. If possible, the new...
• Thermal compound between the CPU & heat sink. The thermal compound increases the efficiency of heat transfer from the CPU to the heat sink by filling any tiny gaps between the two. ... Name these ports. PS/2, USB, Optical Audio,...
• S7L2. Students will describe the structure and function of cells, tissues, organs, and organ systems. Explain that cells take in nutrients in order to grow and divide and to make needed materials.