100014 求扇形圆柱表面积体积已知半径度数高

<?php
header('Content-Type: text/html; charset=utf-8');
define ('ROOT', $_SERVER['DOCUMENT_ROOT']);
include ROOT.'/assets/php/head.php';

$tit= '求扇形圆柱表面积体积已知半径度数高';
//已知半径10，度数90，高30
$val='10 90 30';
$img='';

//调用方法
mill($val,$img,$tit);

/**
 * mill 是磨粉机的方法
 * $val 传值过来计算，以空格分割成数值
 * $img 自定义图片名，默认以文件名为图片名
 * $tit 标题名
 * */
function mill($val,$img,$tit){
    //初始化
    include ROOT.'/assets/php/init.php';
    imgt($img,$tit);

    //设置小数点保留位数 
    bcscale (2);
    $pi = round(pi(),2);
    
    //以空格分割成数值
    $vals = expl($val);
    $r = evev($vals[0]);
    $o = evev($vals[1]);
    $h = evev($vals[2]);

    //已知条件
    $know = array();
    array_push($know, $val);
    $v0 = eveq($vals[0]);
    array_push($know, "半径：$v0");
    $v1 = eveq($vals[1]);
    array_push($know, "度数：$v1{$math['o']}");
    $v2 = eveq($vals[2]);
    array_push($know, "高：$v2");

    //计算步骤
    $step = array();
    array_push($step, "扇形圆柱的表面积：");
    array_push($step, "{$math['eqs']} $pi{$math['mul']}2{$math['mul']}$r{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']}{$math['mul']}$h{$math['add']}$pi{$math['mul']}$r{$math['sup2']}{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']}{$math['mul']}2{$math['add']}$r{$math['mul']}$h{$math['mul']}2");
    $o360 = bcdiv($o, 360);
    array_push($step, "{$math['eqs']} $pi{$math['mul']}2{$math['mul']}$r{$math['mul']}$o360{$math['mul']}$h{$math['add']}$pi{$math['mul']}$r{$math['sup2']}{$math['mul']}$o360{$math['mul']}2{$math['add']}$r{$math['mul']}$h{$math['mul']}2");
    $r2 = bcmul($r, 2);
    $rr = bcmul($r, $r);
    array_push($step, "{$math['eqs']} $pi{$math['mul']}$r2{$math['mul']}$o360{$math['mul']}$h{$math['add']}$pi{$math['mul']}$rr{$math['mul']}$o360{$math['mul']}2{$math['add']}$r{$math['mul']}$h{$math['mul']}2");
    $pir2 = bcmul($pi, $r2);
    $pirr = bcmul($pi, $rr);
    $rh = bcmul($r, $h);
    array_push($step, "{$math['eqs']} $pir2{$math['mul']}$o360{$math['mul']}$h{$math['add']}$pirr{$math['mul']}$o360{$math['mul']}2{$math['add']}$rh{$math['mul']}2");
    $pir2o360 = bcmul($pir2, $o360);
    $pirro360 = bcmul($pirr, $o360);
    array_push($step, "{$math['eqs']} $pir2o360{$math['mul']}$h{$math['add']}$pirro360{$math['mul']}2{$math['add']}$rh{$math['mul']}2");
    $pir2o360h = bcmul($pir2o360, $h);
    $pirro3602 = bcmul($pirro360, 2);
    $rh2 = bcmul($rh, 2);
    array_push($step, "{$math['eqs']} $pir2o360h{$math['add']}$pirro3602{$math['add']}$rh2");
    $pir2o360hpirro3602 = bcadd($pir2o360h, $pirro3602);
    array_push($step, "{$math['eqs']} $pir2o360hpirro3602{$math['add']}$rh2");
    $S = bcadd($pir2o360hpirro3602, $rh2);
    array_push($step, "{$math['eqs']} $S");

    array_push($step, "扇形圆柱的体积：");
    array_push($step, "{$math['eqs']} $pi{$math['mul']}$r{$math['sup2']}{$math['mul']}$h{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']}");
    $o360 = bcdiv($o, 360);
    array_push($step, "{$math['eqs']} $pi{$math['mul']}$r{$math['sup2']}{$math['mul']}$h{$math['mul']}$o360");
    $rr = bcmul($r, $r);
    array_push($step, "{$math['eqs']} $pi{$math['mul']}$rr{$math['mul']}$h{$math['mul']}$o360");
    $pirr = bcmul($pi, $rr);
    array_push($step, "{$math['eqs']} $pirr{$math['mul']}$h{$math['mul']}$o360");
    $pirrh = bcmul($pirr, $h);
    array_push($step, "{$math['eqs']} $pirrh{$math['mul']}$o360");
    $V = bcmul($pirrh, $o360);
    array_push($step, "{$math['eqs']} $V");

    //算出结果
    $ends = array();
    array_push($ends, "扇形圆柱的表面积：$S");
    array_push($ends, "扇形圆柱的体积：$V");

    //公式表示
    $home = array();
    array_push($home, "扇形圆柱的表面积：S{$math['eq']}2{$math['pi']}rh{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['sol']}360{$math['o']}{$math['rpar']}{$math['add']}2{$math['pi']}r{$math['sup2']}{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['sol']}360{$math['o']}{$math['rpar']}{$math['add']}2rh");
    array_push($home, "扇形圆柱的体积：V{$math['eq']}{$math['pi']}r{$math['sup2']}h{$math['mul']}{$math['lpar']}$o{$math['o']}{$math['sol']}360{$math['o']}{$math['rpar']}");

    //公式说明
    $info = array();
    array_push($info, "扇形圆柱的表面积 {$math['eq']} 一个侧面积 {$math['mul']} {$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']} {$math['add']} 两个底面圆面积 {$math['mul']} {$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']} {$math['add']} 一个截面积");
    array_push($info, "扇形圆柱的体积 {$math['eq']} 圆周率 {$math['mul']} 半径的平方 {$math['mul']} 高 {$math['mul']} {$math['lpar']}$o{$math['o']}{$math['div']}360{$math['o']}{$math['rpar']}。");

    know($know);
    ends($ends);
    home($home);
    step($step);
    info($info);
}
?>
<?php include ROOT.'/assets/php/foot.php'; ?>

结果：

☁参考上图[2022-11-21]

☀求扇形圆柱表面积体积已知半径度数高
10 90 30
半径：10
度数：90°
高：30

♠算出结果
扇形圆柱的表面积：1228.00
扇形圆柱的体积：2355.00

♦公式表示
扇形圆柱的表面积：S=2πrh×(90°/360°)+2πr²×(90°/360°)+2rh
扇形圆柱的体积：V=πr²h×(90°/360°)

♣计算步骤
扇形圆柱的表面积：
≈ 3.14×2×10×(90°÷360°)×30+3.14×10²×(90°÷360°)×2+10×30×2
≈ 3.14×2×10×0.25×30+3.14×10²×0.25×2+10×30×2
≈ 3.14×20.00×0.25×30+3.14×100.00×0.25×2+10×30×2
≈ 62.80×0.25×30+314.00×0.25×2+300.00×2
≈ 15.70×30+78.50×2+300.00×2
≈ 471.00+157.00+600.00
≈ 628.00+600.00
≈ 1228.00
扇形圆柱的体积：
≈ 3.14×10²×30×(90°÷360°)
≈ 3.14×10²×30×0.25
≈ 3.14×100.00×30×0.25
≈ 314.00×30×0.25
≈ 9420.00×0.25
≈ 2355.00

♥公式解释
扇形圆柱的表面积 = 一个侧面积 × (90°÷360°) + 两个底面圆面积 × (90°÷360°) + 一个截面积
扇形圆柱的体积 = 圆周率 × 半径的平方 × 高 × (90°÷360°)。