The given solid is a cylinder.
<jsxgpre id="Solution_41729_1" alt="given cylinder" 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:[10,100] };
var p1 = b.node(5.69,5.08); /*centre of the upper base*/
var p2 = b.node(7.62,5.03);/*right side of the upper base*/
var p3 = b.node(3.75,5.13);/*left side of the upper base*/
var p4 = b.point(3.65,2,{fillColor:"black"});/*center of the lower base*/
var p5 = b.node(5.59,1.95);/*right side of the lower base*/
var p6 = b.node(1.71,2.05);/*left side of the lower base*/
var n = b.node(5.69,5.61,{});/*this is a point on the upper side of the upper base, just here to make b.trim() work*/
var h = b.node(7.62,1.95);/*point where the height is shown (the right-most one)*/
var radius = b.segment(p4,p5,{strokeColor:'red'});
var h1 = b.segment(p5,h,{strokeColor:'red', dash:3});
var h2 = b.segment(p2,h,{strokeColor:'red', dash:3});/*the dashed segments showing the height*/
var angle = b.angleMarker(p2,h,p5,{});
var g1 = b.node(4.63,2);
var g2 = b.node(4.9,1.17,{});
var seg = b.segment(g1,g2,{strokeColor:'gray',layer:13}); /*the segment between the radius and its length*/
/*segments to draw the sides of the cylinder:*/
var seg1 = b.segment(p3,p6,opt1);
var seg2 = b.segment(p2,p5,opt1);
var ellipse1 = b.ellipse(p1,1.94,0.53,{fillColor:"rgb(229,192,98)",layer:12,strokeColor:"goldenrod"});
var lower = b.ellipse(p4,1.94,0.53,{fillColor:"rgb(229,192,98)", startAngle:0, endAngle:180, dash:3,strokeColor:"goldenrod"});
var lower2 = b.ellipse(p4,1.94,0.53,{fillColor:"rgb(229,192,98)", startAngle:180, endAngle:360,strokeColor:"goldenrod"});/*broken into two to get one part to be shaded and other to be not*/
var polygon1 = b.polygon([p5,p2,p3,[1.71,1.95]],{fillColor:"rgb(229,192,98)", borders:{visible:false}});
var grad = b.gradient(lower,off);
var grad = b.gradient(polygon1,off);
var grad = b.gradient(lower2,off);
var txt1 = b.segmentText(h2,{name:'12\\ \\text{m}', distance:0.6});
var txt2 = b.txt(5,0.85,'6\\ \\text{m}',{});
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
By Cavalieri's Principle, the formula still holds true for oblique cylinders. Since we are given both the radius and height of the cylinder, we can substitute them into the formula and calculate V.
