CAT Exam > CAT Questions > Slant height of the cone is 25 cm. Diameter o...
Start Learning for Free
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).
- a)1500π
- b)6000π
- c)1565π
- d)3125π
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times t...
Let x be the height of the cone.
∴ Diameter = 3x/2
∴ Diameter = 3x/2
∴ Radius = 3x/4
So we get,
252 = x2 + (3x/4)2
252 = x2 + (3x/4)2
∴ x = 20 cm
∴ Radius of the cone = (3 x 20)/4 = 15 cm
Volume of the cone = (1/3) x π x 152 x 20 = 1500π cm3
Hence, option 1.
Hence, option 1.
Most Upvoted Answer
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times t...
Let x be the height of the cone.
∴ Diameter = 3x/2
∴ Diameter = 3x/2
∴ Radius = 3x/4
So we get,
252 = x2 + (3x/4)2
252 = x2 + (3x/4)2
∴ x = 20 cm
∴ Radius of the cone = (3 x 20)/4 = 15 cm
Volume of the cone = (1/3) x π x 152 x 20 = 1500π cm3
Hence, option 1.
Hence, option 1.
Free Test
FREE
| Start Free Test |
Community Answer
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times t...
Given information:
- Slant height of the cone = 25 cm
- Diameter of the cone = 3/2 times the height of the cone
To find: Volume of the cone
Let's solve the problem step by step.
Step 1: Finding the height of the cone
We know that the diameter of the cone is 3/2 times the height of the cone.
Let's assume the height of the cone as h.
So, the diameter = (3/2)h
Radius = (1/2) * diameter = (1/2) * (3/2)h = (3/4)h
We can use the Pythagorean theorem to find the slant height of the cone.
Slant height (l) = √(r^2 + h^2)
Given that slant height (l) = 25 cm
Substituting the values, we get:
25 = √((3/4h)^2 + h^2)
625 = (9/16)h^2 + h^2
625 = (25/16)h^2
h^2 = (625 * 16) / 25
h^2 = 400
h = √400
h = 20 cm
So, the height of the cone is 20 cm.
Step 2: Finding the volume of the cone
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r^2 * h
where r is the radius and h is the height.
We already know the height of the cone, which is 20 cm.
Substituting the values, we get:
Volume = (1/3) * π * (3/4h)^2 * h
= (1/3) * π * (9/16 * 20)^2 * 20
= (1/3) * π * 9/16 * 20 * 20
= (1/3) * π * 9 * 25
= (3/3) * π * 9 * 25
= 3π * 9 * 25
= 675π
Approximating π as 22/7, we get:
Volume ≈ 675 * 22/7
≈ 1500
Therefore, the volume of the cone is approximately 1500 cm^3.
- Slant height of the cone = 25 cm
- Diameter of the cone = 3/2 times the height of the cone
To find: Volume of the cone
Let's solve the problem step by step.
Step 1: Finding the height of the cone
We know that the diameter of the cone is 3/2 times the height of the cone.
Let's assume the height of the cone as h.
So, the diameter = (3/2)h
Radius = (1/2) * diameter = (1/2) * (3/2)h = (3/4)h
We can use the Pythagorean theorem to find the slant height of the cone.
Slant height (l) = √(r^2 + h^2)
Given that slant height (l) = 25 cm
Substituting the values, we get:
25 = √((3/4h)^2 + h^2)
625 = (9/16)h^2 + h^2
625 = (25/16)h^2
h^2 = (625 * 16) / 25
h^2 = 400
h = √400
h = 20 cm
So, the height of the cone is 20 cm.
Step 2: Finding the volume of the cone
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r^2 * h
where r is the radius and h is the height.
We already know the height of the cone, which is 20 cm.
Substituting the values, we get:
Volume = (1/3) * π * (3/4h)^2 * h
= (1/3) * π * (9/16 * 20)^2 * 20
= (1/3) * π * 9/16 * 20 * 20
= (1/3) * π * 9 * 25
= (3/3) * π * 9 * 25
= 3π * 9 * 25
= 675π
Approximating π as 22/7, we get:
Volume ≈ 675 * 22/7
≈ 1500
Therefore, the volume of the cone is approximately 1500 cm^3.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
Question Description
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer?.
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect 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 Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Slant height of the cone is 25 cm. Diameter of the cone is 3/2 times the height of the cone. Find the volume of the cone (in cm3).a)1500πb)6000πc)1565πd)3125πCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup