{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Chapter 8: Computation of volume"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-241  pb-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10.215, 14.84375, 28.433749999999996, 34.375, 23.633750000000003, 16.23375, 9.58375)\n",
      "by trapezoidal rule\n",
      "('V=', 5096.775, 'meter cube')\n",
      "by prismoidal rule\n",
      "('V=', 5143.25, 'meter cube')\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "h1=0.90;h2=1.25;h3=2.15;h4=2.50;h5=1.85;h6=1.35;h7=0.85;\n",
    "\n",
    "b=10;\n",
    "sh=1.5;\n",
    "\n",
    "h=40;\n",
    "\n",
    "d1=(b+(sh*h1))*h1;\n",
    "d2=(b+(sh*h2))*h2;\n",
    "d3=(b+(sh*h3))*h3;\n",
    "d4=(b+(sh*h4))*h4;\n",
    "d5=(b+(sh*h5))*h5;\n",
    "d6=(b+(sh*h6))*h6;\n",
    "d7=(b+(sh*h7))*h7;\n",
    "\n",
    "print(d1,d2,d3,d4,d5,d6,d7)\n",
    "print('by trapezoidal rule');\n",
    "v=(h/2)*(d1+d7+2*(d2+d3+d4+d5+d6));\n",
    "print('V=',v,'meter cube');\n",
    "\n",
    "print('by prismoidal rule');\n",
    "\n",
    "v1=(h/3)*(d1+d7+4*(d2+d4+d6)+2*(d3+d5));\n",
    "\n",
    "print('V=',v1,'meter cube');\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-241,242  pb-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(19.736842105263158, 29.487179487179485, 19.047619047619047, 23.214285714285715)\n",
      "(7.125, 11.845, 7.68, 13.78, 16.5, 7.125)\n",
      "from chainage 0 to 50\n",
      "(70.3125, 179.3165955128205)\n",
      "from chainage 50 to 100\n",
      "(78.74925714285715, 174.63782051282053)\n",
      "from chainage 100 to 150\n",
      "(73.14285714285714, 213.2455)\n",
      "from chainage 150 to 200\n",
      "(221.13535714285715, 159.94642857142858)\n",
      "from chainage 200 to 250\n",
      "590.625\n",
      "('total cutting =', 1033.9649714285715)\n",
      "('total fitting=', 727.1463445970695)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "h1=0.75;h2=1.15;h3=0.80;h4=1.30;h5=1.5;h6=0.75\n",
    "b=8;sh=2;\n",
    "\n",
    "x1=(50*h1)/(h1+h2);\n",
    "x2=(50*h2)/(h2+h3);\n",
    "x3=(50*h3)/(h4+h3);\n",
    "x4=(50*h4)/(h4+h5);\n",
    "print(x1,x2,x3,x4);\n",
    "\n",
    "a1=(b+(sh*h1))*h1;\n",
    "a2=(b+(sh*h2))*h2;\n",
    "a3=(b+(sh*h3))*h3;\n",
    "a4=(b+(sh*h4))*h4;\n",
    "a5=(b+(sh*h5))*h5;\n",
    "a6=(b+(sh*h6))*h6;\n",
    "print(a1,a2,a3,a4,a5,a6)\n",
    "\n",
    "print('from chainage 0 to 50');\n",
    "c1=(a1/2)*(x1);\n",
    "f1=(a2/2)*(x2+0.79);\n",
    "print(c1,f1);\n",
    "\n",
    "\n",
    "\n",
    "print('from chainage 50 to 100');\n",
    "f2=(a2/2)*(x2);\n",
    "c2=(a3/2)*(x3+1.46);\n",
    "print(c2,f2);\n",
    "\n",
    "print('from chainage 100 to 150');\n",
    "c3=(a3/2)*(x3);\n",
    "f3=(a4/2)*(30.95);\n",
    "print(c3,f3);\n",
    "\n",
    "print('from chainage 150 to 200');\n",
    "f4=(a4/2)*(x4);\n",
    "c4=(a5/2)*(x4+3.59);\n",
    "print(c4,f4);\n",
    "\n",
    "print('from chainage 200 to 250');\n",
    "c5=((a1+a5)/2)*50;\n",
    "\n",
    "print(c5);\n",
    "\n",
    "tc=c1+c2+c3+c4+c5;\n",
    "tf=f1+f2+f3+f4;\n",
    "\n",
    "print('total cutting =',tc);\n",
    "print('total fitting=',tf);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-244  pb-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(26.25, 11.5625, 8.5025, 15.9225, 22.44, 30.9225, 6.5625)\n",
      "('volume=', 5472.125)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "h=50;\n",
    "h1=2.50;h2=1.25;h3=0.95;h4=1.65;h5=2.20;h6=2.85;h7=0.75;\n",
    "b=8;sh=1;\n",
    "\n",
    "\n",
    "a1=(b+(sh*h1))*h1;\n",
    "a2=(b+(sh*h2))*h2;\n",
    "a3=(b+(sh*h3))*h3;\n",
    "a4=(b+(sh*h4))*h4;\n",
    "a5=(b+(sh*h5))*h5;\n",
    "a6=(b+(sh*h6))*h6;\n",
    "a7=(b+(sh*h7))*h7;\n",
    "\n",
    "print(a1,a2,a3,a4,a5,a6,a7);\n",
    "\n",
    "v=(h/3)*(a1+a7+4*(a2+a4+a6)+2*(a3+a5));\n",
    "\n",
    "\n",
    "print('volume=',v);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-245  pb-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "according to trapezoidal rule\n",
      "('volume =', 330375.0)\n",
      "according to prismoidal rule\n",
      "('volume =', 330250.0)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "a1=2050;a2=8400;a3=16300;a4=24600;a5=31500;\n",
    "\n",
    "h=5;\n",
    "\n",
    "print('according to trapezoidal rule')\n",
    "\n",
    "v1=(h/2)*(a1+a5+2*(a2+a3+a4));\n",
    "\n",
    "print('volume =',v1);\n",
    "\n",
    "print('according to prismoidal rule')\n",
    "\n",
    "v2=(h/3)*(a1+a5+4*(a2+a4)+2*(a3));\n",
    "\n",
    "print('volume =',v2)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-245,246  pb-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bottom section\n",
      "('area A1=', 1200)\n",
      "mid section\n",
      "('area A2=', 2000.0)\n",
      "top section\n",
      "('area A3=', 30000)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "print('bottom section')\n",
    "L=40;\n",
    "B=30;\n",
    "a1=L*B;\n",
    "print('area A1=',a1)\n",
    "\n",
    "print('mid section')\n",
    "b=40;\n",
    "sh=2.5;\n",
    "\n",
    "l=L+2*2*sh;\n",
    "b=B+2*2*sh;\n",
    "a2=l*b;\n",
    "print('area A2=',a2);\n",
    "\n",
    "print('top section')\n",
    "sh=5;\n",
    "\n",
    "l1=L+2*sh;\n",
    "b1=B*2*2*sh;\n",
    "a3=l1*b1;\n",
    "print('area A3=',a3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-246,247  pb-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first section\n",
      "(6.666666666666666, 5.454545454545455)\n",
      "('area A1=', 20.36363636363636)\n",
      "second section\n",
      "(7.777777777777778, 6.363636363636363)\n",
      "('area A2=', 33.494949494949495)\n",
      "third section\n",
      "(8.88888888888889, 7.2727272727272725)\n",
      "('area A3=', 48.64646464646465)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "b=8;\n",
    "h=2;\n",
    "n=10;\n",
    "s=1;\n",
    "\n",
    "print('first section');\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a1=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A1=',a1);\n",
    "\n",
    "print('second section');\n",
    "b=8;h=3;n=10;s=1;\n",
    "\n",
    "\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a2=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A2=',a2);\n",
    "\n",
    "print('third section');\n",
    "b=8;h=4;n=10;s=1;\n",
    "\n",
    "\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a3=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A3=',a3);\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-247,248  pb-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first section\n",
      "(6.666666666666667, 5.454545454545454)\n",
      "('area A1=', 11.36363636363636)\n",
      "second section\n",
      "(8.75, 5.833333333333333)\n",
      "('area A2=', 26.041666666666664)\n",
      "third section\n",
      "(7.428571428571429, 5.777777777777778)\n",
      "('area A3=', 17.920634920634917)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "b=10;\n",
    "h=1;\n",
    "n=10;\n",
    "s=1;\n",
    "\n",
    "print('first section');\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a1=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A1=',a1);\n",
    "\n",
    "print('second section');\n",
    "b=10;h=2;n=5;s=1;\n",
    "\n",
    "\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a2=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A2=',a2);\n",
    "\n",
    "print('third section');\n",
    "b=10;h=1.5;n=8;s=1;\n",
    "\n",
    "\n",
    "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n",
    "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n",
    "\n",
    "a3=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n",
    "print(b1,b2)\n",
    "\n",
    "print('area A3=',a3);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-248  pb-8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at station 1\n",
      "('area=', 14.25)\n",
      "at station 2\n",
      "('area=', 18.975)\n",
      "('v=', 830.625, 'cp=', 0.20833333333333262)\n",
      "('correct volume =', 830.4166666666666)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "print('at station 1');\n",
    "h=1;h1=2.55;h2=0.95;b=9;b1=7.5;b2=5.25;\n",
    "w1=b1+b2\n",
    "a=(((h/2)*(b1+b2))+((b/4)*(h1+h2)));\n",
    "print('area=',a)\n",
    "\n",
    "print('at station 2');\n",
    "h=1.5;h1=2.8;h2=1.35;b=9;b1=8.1;b2=4.75;\n",
    "\n",
    "a1=(((h/2)*(b1+b2))+((b/4)*(h1+h2)));\n",
    "d=50;\n",
    "k=10.01;\n",
    "v=(d/2)*(a+a1);\n",
    "w2=b1+b2\n",
    "print('area=',a1)\n",
    "h2=1;\n",
    "h1=1.5;\n",
    "cp=(d/12)*(h1-h2)*(w2-w1);\n",
    "\n",
    "\n",
    "cv=v-cp;\n",
    "print('v=',v,'cp=',cp)\n",
    "print('correct volume =',cv);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-249  pb-9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "section 1\n",
      "(7.03125, 1.0416666666666667)\n",
      "section 2\n",
      "(9.03125, 0.375)\n",
      "('vc=', 401.5625, 'vf=', 35.41666666666667)\n",
      "('corrected volume (in cutting)=', 400.5208333333333)\n",
      "('corrected volume(in filling)', 34.027777777777786)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "print('section 1')\n",
    "b=10;n=5;s=1;s1=2;\n",
    "d=50;h1=0.5;h2=0.7;\n",
    "\n",
    "ac=0.5*(((0.5*b+n*h1)*(0.5*b+n*h1))/(n-s));\n",
    "\n",
    "af=0.5*(((0.5*b-n*h1)*(0.5*b-n*h1))/(n-s1));\n",
    "\n",
    "print(ac,af)\n",
    "\n",
    "\n",
    "print('section 2')\n",
    "\n",
    "\n",
    "ac1=0.5*(((0.5*b+n*h2)*(0.5*b+n*h2))/(n-s));\n",
    "\n",
    "af1=0.5*(((0.5*b-n*h2)*(0.5*b-n*h2))/(n-s1));\n",
    "D=50;\n",
    "print(ac1,af1)\n",
    "vc=((ac+ac1)/2)*D;\n",
    "vf=((af+af1)/2)*D;\n",
    "\n",
    "print('vc=',vc,'vf=',vf);\n",
    "\n",
    "D=50;\n",
    "pcc=(D/(12*(n-s)))*(n*n*(h1-h2)*(h1-h2));\n",
    "\n",
    "\n",
    "pcf=(D/(12*(n-s1)))*(n*n*(h1-h2)*(h1-h2));\n",
    "\n",
    "\n",
    "cvc=vc-pcc;\n",
    "cvf=vf-pcf;\n",
    "\n",
    "print('corrected volume (in cutting)=',cvc);\n",
    "\n",
    "print('corrected volume(in filling)',cvf)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### cha-8 page-251  pb-10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at station 1\n",
      "(40.2, 82.475)\n",
      "('area =', 21.137499999999996)\n",
      "at station 2\n",
      "(53.7, 105.675)\n",
      "('area =', 25.987499999999997)\n",
      "volume by average end area rule\n",
      "('volume=', 1178.1249999999998)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from __future__ import division\n",
    "\n",
    "import math\n",
    "\n",
    "a1=0;a2=3.0;\n",
    "b1=2.20;b2=5.50;\n",
    "c1=1.75;c2=3.0;\n",
    "d1=1.5;d2=0;\n",
    "e1=4.75;e2=5.25;\n",
    "f1=6.40;f2=7.30;\n",
    "g1=0;g2=3.0;\n",
    "\n",
    "print('at station 1')\n",
    "sp=(e1*d2)+(f1*e2)+(d2*f2)+(c1*d2)+(b1*c2)+(a1*b2);\n",
    "\n",
    "sq=(e2*d1)+(e1*f2)+(f1*g2)+(d1*c2)+(c1*b2)+(b1*a2);\n",
    "\n",
    "area1=0.5*(sp-sq)\n",
    "area1=abs(area1);\n",
    "print(sp,sq)\n",
    "print('area =',area1)\n",
    "\n",
    "a1=0;a2=3.0;\n",
    "b1=3.1;b2=5.25;\n",
    "c1=2.20;c2=3.0;\n",
    "d1=2;d2=0;\n",
    "e1=5.25;e2=6;\n",
    "f1=7.40;f2=8.5;\n",
    "g1=0;g2=3.0;\n",
    "print('at station 2')\n",
    "sp1=(e1*d2)+(f1*e2)+(d2*f2)+(c1*d2)+(b1*c2)+(a1*b2);\n",
    "\n",
    "sq1=(d1*e2)+(e1*f2)+(f1*g2)+(d1*c2)+(c1*b2)+(b1*a2);\n",
    "print(sp1,sq1)\n",
    "\n",
    "\n",
    "area2=0.5*(sp1-sq1)\n",
    "area2=abs(area2);\n",
    "print('area =',area2)\n",
    "\n",
    "print('volume by average end area rule')\n",
    "v=50*((area1+area2)/2);\n",
    "print('volume=',v)\n"
   ]
  }
 ],
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