CAT Question > The sum of radii spheres A and B is 14 cm, t...
Related Test
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?
Answers
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 =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.
 | View courses related to this question | Explore CAT courses |
Explore CAT courses View courses related to this question |  |
| 1 Crore+ students have signed up on EduRev. Have you? |
Similar CAT Doubts
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice CAT tests.
Top Courses for CAT
Do you know? How Toppers prepare for CAT Exam
With help of the best CAT teachers & toppers, We have prepared a guide for student who are
preparing for CAT : 15 Steps to clear CAT Exam
Download free EduRev App
Track your progress, build streaks, highlight & save important lessons and more!
(Scan QR code)
|
|
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.
|
© EduRev
|
Education Revolution
|
Follow Us
|
