The sum of radii spheres A and B is 14 cm, t...
The sum of radii spheres A and B is 14 cm, the radius of A being larger than that of B. The difference between their surface areas is 112π. What is the ratio of the volumes of A and B?
The sum of radii spheres A and B is 14 cm, the radius of A being larg...
Given
The Difference between the surface area of the spheres is 112π
The sum of the radii of spheres of A and B is 14 cm
As we know,
Area of a sphere =4πr2 (where ' r′ is the radius of the sphere)
Volume of a sphere
= (4/3)πr3
Let the radius of the circle A be ′a′
Let the radius of the circle B be ' b '
Difference of the surface area of the circle is 112π
4πa2 − 4πb2 = 112π
(a + b)⋅(a − b) = 28
a − b = 2 [Given, (a + b) = 2]
a + b = 14… (i)
a − b = 2… (ii)
Solving equation (i) and (ii)
⇒ a = 8 and b = 6
So,
Volume of sphere with radius a cm : volume of sphere with radius b cm=4πa3:4πb3
= 83:63
= 512:216
= 64:27
∴ The ratio of the volume will be 64:27.
Hence, the correct answer is 64:27.
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The sum of radii spheres A and B is 14 cm, the radius of A being larger than that of B. The difference between their surface areas is 112π. What is the ratio of the volumes of A and B?Correct answer is '64 : 27'. Can you explain this answer?
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