MAT136H1 Lecture 23: 8.1 Areas and Volumes & 8.2 Applications to Geometry
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8iareasfvolg. com ft pute thevolume of a square base pyramid base 756 ft 756ft ht by h. Step l createhorizontal slicesof thickness oh step 2 bottom layer h 0 volumeof dies 5oh step 3 6. Let s solelength at ht h volumeof die at ht sci 481 h. Sioh__ 481 hi h hi comes from the fact that you are dividing hetotal ht into n pieces. H hj. ch obtain thegeneral formula for volume of the square grand. _nhl comes fromthepythagorastherom h2 r2 122 r jr2 h. 8. 2appkatonstg g. se up def integrals to find the volumeobtained byregion bluff rotated about the xaxis giolmsgnfon fgzs. tl rout h. Riout rinj. cox isgivenby y 5 anygun point. Step5 unite up sum f approximation step 6 volumej rin volume riut r. in ox rid. ch x 15 55 x i55 i. 0 y 5 fit rout 5 5 r n 5. Temsofa. gg muluequationeasien. li so wecan rewrite thepieceunekngth y2t fix. oxy2. 4x jlt fcx arc length e 6 144 .
