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The difference of the volumes of two spheres is 10061 |1/3 cm 3 . If the radius of the smaller sphere be 7 cm , find the difference of the surface area of two spheres .
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Answers
Step-by-step explanation:
Given:-
The difference of the volumes of two spheres is 10061 |1/3 cm^3 . If the radius of the smaller sphere be 7 cm.
To find:-
Find the difference of the surface area of two spheres .
Solution:-
Let the radius of the bigger sphere be R cm
The radius of the smaller sphere (r)=7 cm
Volume of a sphere = (4/3)πr^3 cubic units
Volume of the bigger sphere =
V1 = (4/3)πR^3 cubic units ----------------(1)
Volume of the smaller sphere = V2
=>(4/3)πr^3
V2=(4/3)π(7)^3 cubic units ------------(2)
The difference of the volumes of the two spheres
=>V1 - V2
=>(4/3)πR^3 - (4/3)π(7)^3
=> (4/3)π(R^3-7^3)
=>(4/3)π(R^3-343)
V1 - V2 = (4/3)π(R^3-343) -------------(3)
According to the given problem
The difference of the volumes of two spheres is 10061 1/3 cm^3
=>V1 - V2 = 10061 1/3 cm^3
=>V1 - V2 =30184/3 cm^3
=>(4/3)π(R^3-343) = 30184/3
On cancelling 3 both sides then
=>4π(R^3-343) = 30184
=>4×(22/7)(R^3-343) =30184
=>(88/7)(R^3-343) =30184
=>88(R^3-343) =30184×7
=>88(R^3-343) = 211288
=>R^3-343 = 211288/88
=>R^3-343 = 2401
=>R^3 = 2401+343
=>R^3 = 2744
=>R^3 = 14×14×14
=>R^3 = (14)^3
=>R = 14
Radius of the bigger sphere = 14 cm
Now
Surface area of the bigger sphere
S1= 4πR^2 sq.units
=>S1 =4×(22/7)×(14)^2 sq.cm
=>S1 = (4×22×14×14)/7
=>S1 = 4×22×14×2
=>S1 = 2464 sq.cm-------------(4)
Surface area of the smaller sphere
S2 = 4πr^2 sq.units
=>S2 = 4×(22/7)×7^2 sq.cm
=>S2 = 4×(22/7)×7×7
=>S2 = (4×22×7×7)/7
=>S2 = 4×22×7 sq.cm
=>S2 = 616 sq.cm -----------(5)
The difference between the surface Areas of the two spheres = S1-S2
=>2464-616
=>1848 sq.cm
Answer:-
The difference of the surface area of two spheres is 1848 sq.cm
Used formulae:-
- Total surface area of a sphere = 4πr^2 sq.units
- Volume of a sphere = (4/3)πr^3 cubic units