Question
Download Solution PDFTwo cones have their heights in the ratio 4 : 3 and the radii of their bases in the ratio 1 : 2. Find the ratio of their volumes.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Heights ratio (h1 : h2) = 4 : 3
Radii ratio (r1 : r2) = 1 : 2
Formula used:
Volume of cone (V) = (1/3)πr2h
Calculation:
Let heights be h1 = 4k and h2 = 3k
Let radii be r1 = k and r2 = 2k
V1 = (1/3)π(k)2(4k)
⇒ V1 = (1/3)πk3 × 4
V2 = (1/3)π(2k)2(3k)
⇒ V2 = (1/3)π4k2 × 3k
⇒ V2 = (1/3)π4k3 × 3
Ratio of volumes = V1 : V2
⇒ (1/3)πk3 × 4 : (1/3)π4k3 × 3
⇒ 4k3 : 12k3
⇒ 1 : 3
∴ The correct answer is option 1.
Last updated on Jun 17, 2025
-> The Staff Selection Commission has released the SSC GD 2025 Result on 17th June 2025 on the official website. Candidates can check if their qualifying status by going through the List.
-> The SSC GD Notification 2026 will be released in October 2025 and the exam will be scheduled in the month of January and February 2026.
-> The SSC GD Merit List is expected to be released soon by the end of April 2025.
-> Previously SSC GD Vacancy was increased for Constable(GD) in CAPFs, SSF, Rifleman (GD) in Assam Rifles and Sepoy in NCB Examination, 2025.
-> Now the total number of vacancy is 53,690. Previously, SSC GD 2025 Notification was released for 39481 Vacancies.
-> The SSC GD Constable written exam was held on 4th, 5th, 6th, 7th, 10th, 11th, 12th, 13th, 17th, 18th, 19th, 20th, 21st and 25th February 2025.
-> The selection process includes CBT, PET/PST, Medical Examination, and Document Verification.
-> The candidates who will be appearing for the 2026 cycle in the exam must attempt the SSC GD Constable Previous Year Papers. Also, attempt SSC GD Constable Mock Tests.