25: Volume and area of solid figures

Example number 25.1, Page number 25.8

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=20;     #length of cuboid(m)
b=10;     #breadth of cuboid(m)
h=8;      #height of cuboid(m)

#Calculation
d=math.sqrt(l**2+b**2+h**2);     #length of diagonal(m)
S=2*((l*b)+(b*h)+(l*h));         #surface area(m**2)
V=l*b*h;      #volume(m**3)

#Result
print "length of diagonal is",round(d,2),"m"
print "surface area is",S,"m**2"
print "volume is",V,"m**3"

length of diagonal is 23.75 m
surface area is 880 m**2
volume is 1600 m**3

Example number 25.2, Page number 25.8

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=12;     #edge(m)

#Calculation
d=e*math.sqrt(3);     #length of diagonal(m)
S=6*(e**2);         #surface area(m**2)
V=e**3;      #volume(m**3)

#Result
print "length of diagonal is",round(d,2),"m"
print "surface area is",S,"m**2"
print "volume is",V,"m**3"

length of diagonal is 20.78 m
surface area is 864 m**2
volume is 1728 m**3

Example number 25.3, Page number 25.8

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
S=726;      #surface area(m**2)

#Calculation
V=(math.sqrt(S/6))**3;      #volume(m**3)

#Result
print "volume is",V,"m**3"

volume is 1331.0 m**3

Example number 25.4, Page number 25.8

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=34.64;       #length of diagonal(m)

#Calculation
V=(d/math.sqrt(3))**3;      #volume(m**3)

#Result
print "volume is",round(V),"m**3"
print "answer varies due to rounding off errors"

volume is 7999.0 m**3
answer varies due to rounding off errors

Example number 25.5, Page number 25.8

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=115;     #length of box(cm)
b=75;     #breadth of box(cm)
h=35;      #height of box(cm)
t=2.5;     #thickness(cm)

#Calculation
IV=l*b*h;      #internal volume(cm**3)
EV=(l+(2*t))*(b+(2*t))*(h+(2*t));      #external volume(cm**3)
V=EV-IV;       #volume of wood(cm**3)

#Result
print "volume of wood is",V,"cm**3"

volume of wood is 82125.0 cm**3

Example number 25.6, Page number 25.9

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=1;      #volume(m**3)
A=10000;   #area(m**2)

#Calculation
x=V*100/A;    #thickness(cm)

#Result
print "thickness is",x,"cm"

thickness is 0.01 cm

Example number 25.7, Page number 25.9

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=54*44*10;     #volume of reservoir(m**3)
R=3/100;        #radius(m)
r=20;     #empty rate(m)

#Calculation
A=math.pi*R**2;    #area of pipe(m**2)
t=V/(A*r);      #time to empty(sec)

#Result
print "time to empty is",round(t/3600,2),"hours"
print "answer varies due to rounding off errors"

time to empty is 116.71 hours
answer varies due to rounding off errors

Example number 25.8, Page number 25.9

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=3000;      #volume of water(m**3)
A=500*300;   #surface area(m**2)

#Calculation
x=V*100/A;    #depth of rain(cm)

#Result
print "depth of rain is",x,"cm"

depth of rain is 2.0 cm

Example number 25.9, Page number 25.9

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=3;
b=4;
c=5;     #sides of a triangle(m)
h=10;    #height of prism(m)

#Calculation
s=(a+b+c)/2;     #semi perimeter(m)
A=math.sqrt(s*(s-a)*(s-b)*(s-c));    #base area(m**2)
V=A*h;      #volume(m**3)

#Result
print "base area is",A,"m**2"
print "volume is",V,"m**3"

base area is 6.0 m**2
volume is 60.0 m**3

Example number 25.10, Page number 25.9

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=7;     #base of triangle(m)
h=24;    #height(m)

#Calculation
A=math.sqrt(3)*(a**2)/4;     #base area(m**2)
V=A*h;    #volume(m**3)

#Result
print "volume is",int(V),"m**3"

volume is 509 m**3

Example number 25.11, Page number 25.10

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=300*10**3;      #height(m)
d=1/9*10**-2;     #diameter(m)
w=270;     #weight of copper wire(kg)
v=0.027;   #per m**3

#Calculation
A=math.pi*(d**2)/4;    #area(m**2)
V=A*h;      #volume of wire(m**3)
W=V*w/v;    #weight of wire(kg) 

#Result
print "weight of wire is",round(W),"kg"
print "answer varies due to rounding off errors"

weight of wire is 2909.0 kg
answer varies due to rounding off errors

Example number 25.12, Page number 25.10

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
r1=6/2;     #radius of 1 pipe(cm)
r2=3/2;     #radius of another pipe(cm)
h=1;    #assume

#Calculation
V1=math.pi*r1**2*h;    #volume of water in supply pipe(cm**3)
V2=math.pi*r2**2*h;    #volume of water in discharge pipe(cm**3)
N=V1/V2;     #number of discharge pipes

#Result
print "number of discharge pipes is",N

number of discharge pipes is 4.0

Example number 25.13, Page number 25.10

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
di=10/100;     #internal diameter(m)
de=12/100;     #external diameter(m)
l=4;    #length(m)
w=7800;    #weight of iron(kg)

#Calculation
V=math.pi*l*(de**2-di**2)/4;    #volume of iron(m**3)
W=V*w;      #weight of iron(kg)

#Result
print "weight of iron is",round(W),"kg"

weight of iron is 108.0 kg

Example number 25.14, Page number 25.10

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=10;    #height of pyramid(m)
d=10;    #length of diagonal(m)

#Calculation
A=d**2/2;    #base area(m**2)
V=A*h/3;     #volume of pyramid(m**3)
a=d/math.sqrt(2);    #side of square(m)
p=4*a;    #base perimeter(m)
x=(h**2)+(a/2)**2;     
l=math.sqrt(x);   #slant height(m)
Ls=p*l/2;   #lateral surface(m**2)

#Result
print "volume of pyramid is",round(V,2),"m**3"
print "lateral surface is",Ls,"m**2"

volume of pyramid is 166.67 m**3
lateral surface is 150.0 m**2