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<!DOCTYPE html>
<html data-require="math graphie">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>Area of a circle</title>
    <script src="../khan-exercise.js"></script>
    <script type="text/javascript">
        var R_COLOR = "purple";
        var D_COLOR = "green";
        var C_COLOR = "blue";
        var K_COLOR = "red";

        function initCircle( R ) {
            var graph = KhanUtil.currentGraph;

            graph.init({
                range: [ [-1.1, 1.1], [-1.1, 1.1] ],
                scale: 100
            });

            graph.circle( [0, 0], 1, { "fill-opacity": 0 } );
        }

        function drawRadius( R ) {
            var graph = KhanUtil.currentGraph;

            graph.line( [0, 0], [1, 0], { "fill": "none", "stroke": R_COLOR } );
            graph.label( [1/2, 0], "\\color{" + R_COLOR + "}{r = " + R + "}", "below" );
        }

        function drawDiameter( R ) {
            var graph = KhanUtil.currentGraph;

            graph.line( [-1, 0], [1, 0], { "stroke": D_COLOR } );
            graph.label( [0, 0], "\\color{" + D_COLOR + "}{d = " + 2 * R + "}", "above" );
        }

        function drawCircumference( R ) {
            var graph = KhanUtil.currentGraph;

            graph.circle( [0, 0], 1, { "stroke": C_COLOR } );
            graph.label( [0, -1], "\\color{" + C_COLOR + "}{c = " + 2 * R + "\\pi}", "below" );
        }

        function drawArea( R ) {
            var graph = KhanUtil.currentGraph;

            var c = graph.circle( [0, 0], 1, { "fill": "#ffcccc", "stroke-width": 0 } );
            $(c.node).insertBefore($(graph.raphael.canvas).find("ellipse")[0]);

            graph.label( [0, 0.5], "\\color{" + K_COLOR + "}{K = " + R*R + "\\pi}", "above" );
        }
    </script>
</head>
<body>
    <div class="exercise">
    <div class="problems">
        <div id="circle-r-to-K">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the radius of a circle is <code>\color{<var>R_COLOR</var>}{<var>R</var>}</code>. What is its area?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>Math.PI * R * R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawRadius( R );
                </div>
                <div>
                    <p>We know <code>K = \pi r^2</code>, so <code>K = \pi \cdot \color{<var>R_COLOR</var>}{<var>R</var>}^2 = \color{<var>K_COLOR</var>}{<var>R * R</var>\pi}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawArea( R );
                    </div>
                </div>
            </div>
        </div>

        <div id="circle-K-to-r">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the area of a circle is <code>\color{<var>K_COLOR</var>}{<var>R === 1 ? "" : R * R</var>\pi}</code>. What is its radius?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawArea( R );
                </div>
                <div>
                    <p>We know <code>K = \pi r^2</code>, so <code>r = \sqrt{K / \pi} = \sqrt{\color{<var>K_COLOR</var>}{<var>R * R</var>\pi} / \pi} = \color{<var>R_COLOR</var>}{<var>R</var>}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawRadius( R );
                    </div>
                </div>
            </div>
        </div>

        <div id="circle-d-to-K">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the diameter of a circle is <code>\color{<var>D_COLOR</var>}{<var>2 * R</var>}</code>. What is its area?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>Math.PI * R * R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawDiameter( R );
                </div>
                <p>First, find the radius: <code>r = d/2 = \color{<var>D_COLOR</var>}{<var>2 * R</var>}/2 = \color{<var>R_COLOR</var>}{<var>R</var>}</code>.</p>
                <div>
                    <p>Now find the area: <code>K = \pi r^2</code>, so <code>K = \pi \cdot \color{<var>R_COLOR</var>}{<var>R</var>}^2 = \color{<var>K_COLOR</var>}{<var>R * R</var>\pi}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawArea( R );
                    </div>
                </div>
            </div>
        </div>

        <div id="circle-K-to-d">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the area of a circle is <code>\color{<var>K_COLOR</var>}{<var>R === 1 ? "" : R * R</var>\pi}</code>. What is its diameter?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>2 * R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawArea( R );
                </div>
                <p>First, find the radius: <code>K = \pi r^2</code>, so <code>r = \sqrt{K / \pi} = \sqrt{\color{<var>K_COLOR</var>}{<var>R * R</var>\pi} / \pi} = \color{<var>R_COLOR</var>}{<var>R</var>}</code>.</p>
                <div>
                    <p>Now find the diameter: <code>d = 2r = 2\cdot \color{<var>R_COLOR</var>}{<var>R</var>} = \color{<var>D_COLOR</var>}{<var>2*R</var>}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawDiameter( R );
                    </div>
                </div>
            </div>
        </div>

        <div id="circle-c-to-K">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the circumference of a circle is <code>\color{<var>C_COLOR</var>}{<var>2 * R</var>\pi}</code>. What is its area?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>Math.PI * R * R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawCircumference( R );
                </div>
                <p>First, find the radius: <code>r = c/2\pi = \color{<var>C_COLOR</var>}{<var>2 * R</var>\pi}/2\pi = \color{<var>R_COLOR</var>}{<var>R</var>}</code>.</p>
                <div>
                    <p>Now find the area: <code>K = \pi r^2</code>, so <code>K = \pi \cdot \color{<var>R_COLOR</var>}{<var>R</var>}^2 = \color{<var>K_COLOR</var>}{<var>R * R</var>\pi}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawArea( R );
                    </div>
                </div>
            </div>
        </div>

        <div id="circle-K-to-c">
            <div class="vars">
                <var id="R">randRange(1, 8)</var>
            </div>

            <div class="question">
                <p>Suppose the area of a circle is <code>\color{<var>K_COLOR</var>}{<var>R === 1 ? "" : R * R</var>\pi}</code>. What is its circumference?</p>
            </div>

            <div class="solution" data-forms="integer, proper, improper, mixed, decimal, pi"><var>Math.PI * 2 * R</var></div>

            <div class="hints">
                <div class="graphie" id="circle">
                    initCircle( R );

                    drawArea( R );
                </div>
                <p>First, find the radius: <code>K = \pi r^2</code>, so <code>r = \sqrt{K / \pi} = \sqrt{\color{<var>K_COLOR</var>}{<var>R * R</var>\pi} / \pi} = \color{<var>R_COLOR</var>}{<var>R</var>}</code>.</p>
                <div>
                    <p>Now find the circumference: <code>c = 2\pi r = 2\pi \cdot \color{<var>R_COLOR</var>}{<var>R</var>} = \color{<var>C_COLOR</var>}{<var>2*R</var>\pi}</code>.</p>

                    <div class="graphie" data-update="circle">
                        drawCircumference( R );
                    </div>
                </div>
            </div>
        </div>
    </div>
    </div>
</body>
</html>
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