The cost of polishing the total surface area of a closed cylindrical tank at the
rate of 20 paise per dm-is 154. If its height is one and a half times the radius
of the base, determine its radius and height.
Answers
Step-by-step explanation:
Given:-
The cost of polishing the total surface area of a closed cylindrical tank at the rate of 20 paise per dm-is 154. and it's height is one and a half times the radius of the base.
To find:-
Determine the radius and height of the cylindrical tank?
Solution:-
Let the radius of the closed cylindrical tank be "r" dm
Then the height of the tank = 1 1/2 times of the radius = 3/2 (r) = 3r/2 dm
Total Cost of polishing the total surface area of the given tank at the rate of 20 paise per dm = Rs. Rs.154
Total Surface Area of the cylindrical tank = 154×100/20
(1 Rupee = 100 paise)
= 7700/10
=770 sq.dm
Total Surface Area of the given tank = 770 sq.dm
Total Surface Area of a cylinder
= 2πr(r+h) sq.units
=>2πr(r+h)=770
=>2(22/7)×r[r+(3r/2)] = 770
=>(44/7)×r×[(2r+3r)/2] = 770
=>(44/7)×r×(5r/2)=770
=>(44×r×5r)/(7×2) = 770
=>44×5r^2 /14 = 770
=>220r^2/14 = 770
=>220 r^2 = 770×14
=>r^2 = (770×14)/220
=>r^2 = 10780/220
=>r^2 = 49
=>r^2 = 7^2
=>r=7 dm
radius = 7 dm
Height = 3r/2 dm
=> 3(7)/2 dm
=>21/2 dm
=>10.5 dm
Height = 10.5 dm
Answer:-
Radius of the closed cylindrical tank
= 7 dm
Height of the closed cylindrical tank
= 10.5 dm
Used formulae:-
- Total Surface Area of a cylinder = 2πr(r+h) sq.units
Where, r = radius of the cylinder
h=Height of the cylinder
π = 22/7