English
Hindi
Bengali
Marathi
Tamil

Question

Download Solution PDF

A solid metallic hemisphere of radius 5.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height (in cm) of the cylinder?

This question was previously asked in
RPF Constable 2024 Official Paper (Held On 03 Mar, 2025 Shift 1)
Download PDF Attempt in App
View all RPF Constable Papers >
  1. 0.625
  2. 0.729
  3. 0.325
  4. 0.468

Answer (Detailed Solution Below)

Option 2 : 0.729
Free Tests
View all Free tests >
Free
RPF Constable Full Test 1
120 Qs. 120 Marks 90 Mins
Start Now

Detailed Solution

Download Solution PDF

Given:

A solid metallic hemisphere of radius 5.4 cm is melted and recast into a right circular cylinder of radius 12 cm.

Formula used:

Volume of hemisphere =

Volume of cylinder =

Calculation:

Volume of hemisphere = Volume of cylinder

=

⇒

⇒

⇒

⇒ 104.976 = 144h

⇒ h =

⇒ h = 0.729

∴ The correct answer is option (2).

Download Solution PDF
Latest RPF Constable Updates

Last updated on Jul 16, 2025

-> More than 60.65 lakh valid applications have been received for RPF Recruitment 2024 across both Sub-Inspector and Constable posts.

-> Out of these, around 15.35 lakh applications are for CEN RPF 01/2024 (SI) and nearly 45.30 lakh for CEN RPF 02/2024 (Constable).

 

-> The Examination was held from 2nd March to 18th March 2025. Check the RPF Exam Analysis Live Updates Here.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Solid Figures Questions

Q1.If the volume of a right circular cone of height 30 cm is 160π cm3, find the diameter of its base.
Q2.A river 20 m deep and 36 m wide is flowing at the rate of 2.7 km/hr. The amount of water (in m3) that runs into the sea per minute is _____.
Q3.The curved surface area of a cylinder is half of its total surface area. If the height is 128 cm, then find the radius (in cm).
Q4.Find the surface area of a sphere whose diameter is equal to 112 cm.
Q5.The volume of a solid cylinder is  5852 cm3 and its height is  38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer)  (Use \(\pi\) = \(\frac{22}{7}\))
Q6. Find the volume (in cm3) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use \(\pi\) = \(\frac{22}{7}\)
Q7.A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is 2/3 full. Find the volume( in cm3) of water in the vessel.
Q8.A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
Q9.The curved surface area of a right circular cone is 5400π cm2, and the diameter of its base is 144 cm. Find the height (in cm) of the cone.

More Mensuration Questions

Q1.Three times the length of a rectangle is equal to seven times its breadth. The area of the rectangle is 2352 sq. cm. What is the area of a square whose perimeter is equal to that of the rectangle?
Q2.The length, width and height of a cuboid are in the ratio 10 : 17 : 14, and its total surface area is 1096 cm2. Find the length (in cm) of the cuboid.
Q3.If the volume of a right circular cone of height 30 cm is 160π cm3, find the diameter of its base.
Q4.A river 20 m deep and 36 m wide is flowing at the rate of 2.7 km/hr. The amount of water (in m3) that runs into the sea per minute is _____.
Q5.The curved surface area of a cylinder is half of its total surface area. If the height is 128 cm, then find the radius (in cm).
Q6.Find the surface area of a sphere whose diameter is equal to 112 cm.
Q7.The area of a rectangle increases by 8 m2 if its length is increased by 5 m and breadth is decreased by 7 m. If the length is decreased by 5 m and breadth is increased by 8 m,  then its area increases by 33 m2. What is the perimeter of the original rectangle (in m)?
Q8.The volume of a solid cylinder is  5852 cm3 and its height is  38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer)  (Use \(\pi\) = \(\frac{22}{7}\))
Q9.The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take \(\pi\) = \(\frac{22}{7}\)
Q10.The sides (in cm) of a right triangle are (x − 13), (x − 26) and x. Its area (in cm2) is:
Suggested Test Series
View All >
Reasoning for All Railway Exams Previous Year Paper Mock Test
753 Total Tests with 1 Free Tests
Start Free Test
RPF Constable Mock Test Series 2024
1197 Total Tests with   3 Free Tests
Start Free Test

More Quantitative Aptitude Questions

Q1.The average weight of 12 bags of rice is 45 kg. When the weights of 3 bags of rice with weights (w+5) kg, (w−15) kg, and (w+40) kg are added, the average weight is increased by 2 kg. Find the value of 'w'.
Q2.The value of a laptop depreciates by 10% every year. The laptop is sold after 3 years at a discount of Rs. 270 on its price at that time. What is the total loss percent incurred after selling the laptop if it was purchased at Rs. 10,000?
Q3.Priya and Rahul started a project together, and after 'k' days, Priya left and Rahul finished the remaining project in 8 days. The time taken by Rahul and Priya alone to complete the whole project are in the ratio 2:1 respectively. If Rahul can complete the entire project in 20 days, then calculate the value of 'k'.
Q4.12 years ago, the sum of the ages of P, Q, and R together was 61 years. The ratio of the present age of P to Q is 2:3, and P is 8 years older than R. If the ratio of the present age of P to S is 5:7, then find the present age of S.
Q5.Three times the length of a rectangle is equal to seven times its breadth. The area of the rectangle is 2352 sq. cm. What is the area of a square whose perimeter is equal to that of the rectangle?
Q6.Two containers X and Y contain a mixture of milk and water. In container X, the ratio of milk to water is 5:2. In container Y, the ratio of milk to water is 3:4. The mixtures from X and Y are mixed together in the ratio 7:5 respectively to form a new mixture. How much milk is present in 84 liters of the new mixture?
Q7.A box contains 6 blue balls, y white balls, and (y + 4) black balls. The probability of selecting a white ball at random is 1/4. If two balls are drawn simultaneously, what is the probability that both balls are black?
Q8.Direction: In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer. I. 12x² + 7x − 12 = 0 II. 8y² − 18y + 9 = 0
Q9.Direction: In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer. I. x² − 35x + 294 = 0 II. y² − 38y + 345 = 0
Q10.Direction: In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer. I. x² − 22x + 105 = 0 II. y² − 20y + 96 = 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： all teen patti master teen patti joy mod apk teen patti - 3patti cards game teen patti real cash game