CAT Exam > CAT Questions > Increasing the height of a cone by 9 units in...
Start Learning for Free
Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.
- a)6 units
- b)7 units
- c)8 units
- d)9 units
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Increasing the height of a cone by 9 units increases its volume by x c...
To solve this problem, we need to use the formulas for the volume of a cone and the relationship between the volume and the radius and height of the cone.
Let's start by calculating the original volume of the cone. The volume of a cone is given by the formula:
V = (1/3)πr^2h
Where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
Let's assume the original radius of the cone is r units. Using the given height of 3 units, the original volume can be written as:
V1 = (1/3)πr^2(3)
Now, let's consider the first scenario where the height is increased by 9 units. The new height would be (3 + 9) = 12 units. The new volume can be calculated as:
V2 = (1/3)πr^2(12)
Since the increase in height of 9 units increases the volume by x cubic units, we can write:
V2 - V1 = x
Substituting the values of V1 and V2, we get:
(1/3)πr^2(12) - (1/3)πr^2(3) = x
Simplifying further:
(1/3)πr^2(12 - 3) = x
(1/3)πr^2(9) = x
Now, let's consider the second scenario where the radius is increased by 6 units. The new radius would be (r + 6) units. The new volume can be calculated as:
V3 = (1/3)π(r + 6)^2(3)
Similarly, we can write:
V3 - V1 = x
Substituting the values of V1 and V3, we get:
(1/3)π(r + 6)^2(3) - (1/3)πr^2(3) = x
Simplifying further:
(1/3)π(r^2 + 12r + 36 - r^2) = x
(1/3)π(12r + 36) = x
Since we have the same value for x in both scenarios, we can equate the expressions for x:
(1/3)πr^2(9) = (1/3)π(12r + 36)
Simplifying further:
r^2(9) = 12r + 36
9r^2 - 12r - 36 = 0
Dividing the equation by 3:
3r^2 - 4r - 12 = 0
Factoring the quadratic equation:
(3r + 2)(r - 6) = 0
Setting each factor equal to zero:
3r + 2 = 0 or r - 6 = 0
Solving for r, we get:
r = -2/3 or r = 6
Since the radius cannot be negative, the original radius of the cone is 6 units. Therefore, the correct answer is option A) 6 units.
Let's start by calculating the original volume of the cone. The volume of a cone is given by the formula:
V = (1/3)πr^2h
Where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
Let's assume the original radius of the cone is r units. Using the given height of 3 units, the original volume can be written as:
V1 = (1/3)πr^2(3)
Now, let's consider the first scenario where the height is increased by 9 units. The new height would be (3 + 9) = 12 units. The new volume can be calculated as:
V2 = (1/3)πr^2(12)
Since the increase in height of 9 units increases the volume by x cubic units, we can write:
V2 - V1 = x
Substituting the values of V1 and V2, we get:
(1/3)πr^2(12) - (1/3)πr^2(3) = x
Simplifying further:
(1/3)πr^2(12 - 3) = x
(1/3)πr^2(9) = x
Now, let's consider the second scenario where the radius is increased by 6 units. The new radius would be (r + 6) units. The new volume can be calculated as:
V3 = (1/3)π(r + 6)^2(3)
Similarly, we can write:
V3 - V1 = x
Substituting the values of V1 and V3, we get:
(1/3)π(r + 6)^2(3) - (1/3)πr^2(3) = x
Simplifying further:
(1/3)π(r^2 + 12r + 36 - r^2) = x
(1/3)π(12r + 36) = x
Since we have the same value for x in both scenarios, we can equate the expressions for x:
(1/3)πr^2(9) = (1/3)π(12r + 36)
Simplifying further:
r^2(9) = 12r + 36
9r^2 - 12r - 36 = 0
Dividing the equation by 3:
3r^2 - 4r - 12 = 0
Factoring the quadratic equation:
(3r + 2)(r - 6) = 0
Setting each factor equal to zero:
3r + 2 = 0 or r - 6 = 0
Solving for r, we get:
r = -2/3 or r = 6
Since the radius cannot be negative, the original radius of the cone is 6 units. Therefore, the correct answer is option A) 6 units.
Free Test
FREE
| Start Free Test |
Community Answer
Increasing the height of a cone by 9 units increases its volume by x c...
Let the initial volume of the cone be
After increasing the radius by 6 units, new volume
After increasing the height by 9 units, new volume
By putting the value of x in equation (i), we get:
9r2 = h[36 + 12r]
After increasing the radius by 6 units, new volume
After increasing the height by 9 units, new volume
By putting the value of x in equation (i), we get:
9r2 = h[36 + 12r]
By putting the value of h in above equation, we get:
9r2 = 3[36 + 12r]
3r2 - 12r - 36 = 0
r2 - 4r - 12 = 0
r2 - 6r + 2r - 12 = 0
r = 6 units
9r2 = 3[36 + 12r]
3r2 - 12r - 36 = 0
r2 - 4r - 12 = 0
r2 - 6r + 2r - 12 = 0
r = 6 units
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer?
Question Description
Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer?.
Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. 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 Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Increasing the height of a cone by 9 units increases its volume by x cubic units. Increasing its radius by 6 units also increases its volume by x cubic units. If the original height is 3 units, then the original radius is _____.a)6 unitsb)7 unitsc)8 unitsd)9 unitsCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup