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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?

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

Radius of A is larger than the radius of B

As we know,

Area of a sphere =4πr^{2} (where ' r′ is the radius of the sphere)

Volume of a sphere

= (4/3)πr^{3}

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

4πa^{2 }− 4πb^{2 }= 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=4πa^{3}:4πb^{3}

= 8^{3}:6^{3}

= 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? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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GivenThe Difference between the surface area of the spheres is 112πThe sum of the radii of spheres of A and B is 14 cmRadius of A is larger than the radius of BAs we know,Area of a sphere =4πr2 (where ' r′ is the radius of the sphere)Volume of a sphere= (4/3)πr3Let 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 112π4πa2 − 4πb2 = 112π(a + b)⋅(a − b) = 28a − b = 2 [Given, (a + b) = 2]a + b = 14… (i)a − b = 2… (ii)Solving equation (i) and (ii)⇒ a = 8 and b = 6So,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.