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diff --git a/Quantitative_Aptitude_for_Competitive_Examinations/Chapter25.ipynb b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter25.ipynb new file mode 100755 index 00000000..15760b75 --- /dev/null +++ b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter25.ipynb @@ -0,0 +1,611 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 25: Volume and area of solid figures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.1, Page number 25.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of diagonal is 23.75 m\n",
+ "surface area is 880 m**2\n",
+ "volume is 1600 m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=20; #length of cuboid(m)\n",
+ "b=10; #breadth of cuboid(m)\n",
+ "h=8; #height of cuboid(m)\n",
+ "\n",
+ "#Calculation\n",
+ "d=math.sqrt(l**2+b**2+h**2); #length of diagonal(m)\n",
+ "S=2*((l*b)+(b*h)+(l*h)); #surface area(m**2)\n",
+ "V=l*b*h; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of diagonal is\",round(d,2),\"m\"\n",
+ "print \"surface area is\",S,\"m**2\"\n",
+ "print \"volume is\",V,\"m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.2, Page number 25.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of diagonal is 20.78 m\n",
+ "surface area is 864 m**2\n",
+ "volume is 1728 m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=12; #edge(m)\n",
+ "\n",
+ "#Calculation\n",
+ "d=e*math.sqrt(3); #length of diagonal(m)\n",
+ "S=6*(e**2); #surface area(m**2)\n",
+ "V=e**3; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of diagonal is\",round(d,2),\"m\"\n",
+ "print \"surface area is\",S,\"m**2\"\n",
+ "print \"volume is\",V,\"m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.3, Page number 25.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume is 1331.0 m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "S=726; #surface area(m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "V=(math.sqrt(S/6))**3; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume is\",V,\"m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.4, Page number 25.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume is 7999.0 m**3\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=34.64; #length of diagonal(m)\n",
+ "\n",
+ "#Calculation\n",
+ "V=(d/math.sqrt(3))**3; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume is\",round(V),\"m**3\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.5, Page number 25.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume of wood is 82125.0 cm**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=115; #length of box(cm)\n",
+ "b=75; #breadth of box(cm)\n",
+ "h=35; #height of box(cm)\n",
+ "t=2.5; #thickness(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "IV=l*b*h; #internal volume(cm**3)\n",
+ "EV=(l+(2*t))*(b+(2*t))*(h+(2*t)); #external volume(cm**3)\n",
+ "V=EV-IV; #volume of wood(cm**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume of wood is\",V,\"cm**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.6, Page number 25.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "thickness is 0.01 cm\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V=1; #volume(m**3)\n",
+ "A=10000; #area(m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "x=V*100/A; #thickness(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"thickness is\",x,\"cm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.7, Page number 25.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time to empty is 116.71 hours\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V=54*44*10; #volume of reservoir(m**3)\n",
+ "R=3/100; #radius(m)\n",
+ "r=20; #empty rate(m)\n",
+ "\n",
+ "#Calculation\n",
+ "A=math.pi*R**2; #area of pipe(m**2)\n",
+ "t=V/(A*r); #time to empty(sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"time to empty is\",round(t/3600,2),\"hours\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.8, Page number 25.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "depth of rain is 2.0 cm\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V=3000; #volume of water(m**3)\n",
+ "A=500*300; #surface area(m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "x=V*100/A; #depth of rain(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"depth of rain is\",x,\"cm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.9, Page number 25.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "base area is 6.0 m**2\n",
+ "volume is 60.0 m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=3;\n",
+ "b=4;\n",
+ "c=5; #sides of a triangle(m)\n",
+ "h=10; #height of prism(m)\n",
+ "\n",
+ "#Calculation\n",
+ "s=(a+b+c)/2; #semi perimeter(m)\n",
+ "A=math.sqrt(s*(s-a)*(s-b)*(s-c)); #base area(m**2)\n",
+ "V=A*h; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"base area is\",A,\"m**2\"\n",
+ "print \"volume is\",V,\"m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.10, Page number 25.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume is 509 m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=7; #base of triangle(m)\n",
+ "h=24; #height(m)\n",
+ "\n",
+ "#Calculation\n",
+ "A=math.sqrt(3)*(a**2)/4; #base area(m**2)\n",
+ "V=A*h; #volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume is\",int(V),\"m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.11, Page number 25.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "weight of wire is 2909.0 kg\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=300*10**3; #height(m)\n",
+ "d=1/9*10**-2; #diameter(m)\n",
+ "w=270; #weight of copper wire(kg)\n",
+ "v=0.027; #per m**3\n",
+ "\n",
+ "#Calculation\n",
+ "A=math.pi*(d**2)/4; #area(m**2)\n",
+ "V=A*h; #volume of wire(m**3)\n",
+ "W=V*w/v; #weight of wire(kg) \n",
+ "\n",
+ "#Result\n",
+ "print \"weight of wire is\",round(W),\"kg\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.12, Page number 25.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of discharge pipes is 4.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r1=6/2; #radius of 1 pipe(cm)\n",
+ "r2=3/2; #radius of another pipe(cm)\n",
+ "h=1; #assume\n",
+ "\n",
+ "#Calculation\n",
+ "V1=math.pi*r1**2*h; #volume of water in supply pipe(cm**3)\n",
+ "V2=math.pi*r2**2*h; #volume of water in discharge pipe(cm**3)\n",
+ "N=V1/V2; #number of discharge pipes\n",
+ "\n",
+ "#Result\n",
+ "print \"number of discharge pipes is\",N"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.13, Page number 25.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "weight of iron is 108.0 kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "di=10/100; #internal diameter(m)\n",
+ "de=12/100; #external diameter(m)\n",
+ "l=4; #length(m)\n",
+ "w=7800; #weight of iron(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "V=math.pi*l*(de**2-di**2)/4; #volume of iron(m**3)\n",
+ "W=V*w; #weight of iron(kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"weight of iron is\",round(W),\"kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 25.14, Page number 25.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume of pyramid is 166.67 m**3\n",
+ "lateral surface is 150.0 m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=10; #height of pyramid(m)\n",
+ "d=10; #length of diagonal(m)\n",
+ "\n",
+ "#Calculation\n",
+ "A=d**2/2; #base area(m**2)\n",
+ "V=A*h/3; #volume of pyramid(m**3)\n",
+ "a=d/math.sqrt(2); #side of square(m)\n",
+ "p=4*a; #base perimeter(m)\n",
+ "x=(h**2)+(a/2)**2; \n",
+ "l=math.sqrt(x); #slant height(m)\n",
+ "Ls=p*l/2; #lateral surface(m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume of pyramid is\",round(V,2),\"m**3\"\n",
+ "print \"lateral surface is\",Ls,\"m**2\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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