If the radius of a sphere is thrice the radius of a hemisphere, then what will be the respective ratio of their volumes?

This question was previously asked in
SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 14 March, 2023 Shift 1)
View all SSC CHSL Papers >
  1. 54 ∶ 1
  2. 27 ∶ 1
  3. 16 ∶ 1
  4. 18 ∶ 1

Answer (Detailed Solution Below)

Option 1 : 54 ∶ 1
Free
SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug 2023 Shift 1)
2.6 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

The radius of the hemisphere: r

Radius of the sphere: 3r

Formula:

Volume of a hemisphere = (2/3)πr3

Volume of a sphere = (4/3)π(radius)3

Calculation:

Let's calculate the respective volumes of the hemisphere and the sphere.

Volume of the hemisphere = (2/3)πr3

Volume of the sphere = (4/3)π(3r)3

Simplifying the expressions:

Volume of the hemisphere = (2/3)πr3

Volume of the sphere = (4/3)π27r3

Now, let's calculate the ratio of the volumes.

The ratio of volumes = (Volume of the sphere) / (Volume of the hemisphere)

= [(4/3)π27r3]/[(2/3)πr3]

= 54

Therefore, the respective ratio of the volumes of the sphere and the hemisphere is 54:1.

Latest SSC CHSL Updates

Last updated on May 28, 2025

-> The SSC has released the SSC CHSL exam calendar for various exams including CHSL 2025 Recruitment. As per the calendar, SSC CHSL Application process will be active from 23rd June 2025 to 18th July 2025. 

-> The Exam Date for the SSC CHSL 2025 will be from 8th September 2025 to 18th September, 2025. 

-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government. 

-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).

-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.  

More Mensuration Questions

Get Free Access Now
Hot Links: teen patti boss teen patti win teen patti apk download teen patti diya teen patti 3a