McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
4. Volumes of Prisms and Cylinders
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Exercise 16 Page 867

Use the formula for the volume of a cylinder.

1413.7 yd^3

Practice makes perfect

The given solid is a cylinder. <jsxgpre id="Solution_41739_1" alt="" static=1> var b=mlg.board([0.0,6.0,10.0,0.0],{desktopSize:"medium",style:"usa",grid:false}); var opt1 = {strokeColor:"goldenrod", layer:12}; var off = {color:["rgb(229,192,98)","rgb(244,228,188)"], offset:[40,100], angle:270 }; /*just to make the gradient simpler later on*/ var p1 = b.point(3.26,3.08,{fillColor:"black",layer:14}); /*the center of the left base*/ var p2 = b.node(8.61,3.08); /*center of the right base*/ b.node(9.55,3.08,{});/*just here to make b.trim() work*/ var ellipse1 = b.ellipse(p1,0.94,1.89,{fillColor:"rgb(229,192,98)",layer:12,strokeColor:"goldenrod"}); var right = b.ellipse(p2,0.94,1.89,{fillColor:"rgb(229,192,98)", startAngle:90, endAngle:270, dash:3,strokeColor:"goldenrod"}); var right2 = b.ellipse(p2,0.94,1.89,{fillColor:"rgb(229,192,98)", startAngle:-90, endAngle:90,strokeColor:"goldenrod"});/*the right one is split into two due to the dashed part*/

var n1 = b.node(3.26,4.97);/*point on the top of the left circle where the radius goes*/ var seg1 = b.segment(p1,n1,{strokeColor:'red',layer:13});/*the radius*/

var s1 = b.node(3.26,1.19); var s2 = b.node(8.65,1.19); var seg1 = b.segment(s1,s2,opt1); var s3 = b.node(3.26,4.97); var s4 = b.node(8.65,4.97); var seg2 = b.segment(s3,s4,opt1);/*top and bottom lines of the cylinder*/

var g1 = b.node(3.25,4); var g2 = b.node(1.93,3.31,{}); var seg = b.segment(g1,g2,{strokeColor:'gray',layer:13});/*the gray segment between the radius and its length*/

var polygon1 = b.polygon([s1,s2,s4,s3],{fillColor:"rgb(229,192,98)", borders:{visible:false}}); var grad = b.gradient(right,off); var grad = b.gradient(polygon1,off); var grad = b.gradient(right2,off); var txt1 = b.txt(6.3,0.8,'18\\ \\text{yd}',{}); var txt2 = b.txt(1.5,3.31,'5\\ \\text{yd}',{}); b.trim(); </jsxgpre> The volume of a cylinder with the radius r and height h can be calculated by the following formula. V=Ï€ r^2 h Since we are given both the radius and height of the cylinder, we can substitute them into the formula and calculate V.

V=Ï€ r^2 h
V=Ï€ ( 5)^2 ( 18)
â–¼
Simplify right-hand side
V=Ï€( 25)( 18)
V=450Ï€
V=1413.71669...
V≈ 1413.7

The approximate volume of the given cylinder is $1413.7 \ \text

{yd}^3.$