A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is:

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 2)
View all SSC CGL Papers >
  1. 6√2 cm
  2. 9 cm
  3. 6 cm
  4. 3√6 cm

Answer (Detailed Solution Below)

Option 2 : 9 cm
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.3 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

The curved surface area of the cone = 2 × base area of cone

Concepts used:

quesImage5679

Formula used

Slant height (l) of cone = √r2 + h2

CSA of cone = πrl

Calculation:

Let the radius of the cone be r units.

πrl = 2πr2

⇒ l = 2r

⇒ r = 6√3/2

⇒ r = 3√3

Slant height (l) of cone = √r2 + h2

⇒ 6√32 = 3√3+ h2

⇒ h2 = 108 - 27 = 81

⇒ h = 9 cm

∴ The answer is 9 cm.

Latest SSC CGL Updates

Last updated on Jul 9, 2025

-> The SSC CGL Notification 2025 for the Combined Graduate Level Examination has been officially released on the SSC's new portal – www.ssc.gov.in.

-> Bihar Police Admit Card 2025 Out at csbc.bihar.gov.in

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The AP DSC Answer Key 2025 has been released on its official website.

-> The UP ECCE Educator 2025 Notification has been released for 8800 Posts.

More Mensuration Questions

Get Free Access Now
Hot Links: teen patti noble teen patti gold real cash teen patti bindaas