Question
Download Solution PDFThe internal and external radii of a hollow spherical shell are 4 cm and 8 cm, respectively. It is melted and recast into a solid right circular cylinder of height \(9 \frac{1}{3}\) cm. What is curved surface area (in cm2) of the cylinder?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Hollow spherical shell:
Internal radius (r1) = 4 cm
External radius (r2) = 8 cm
Cylinder:
Height (h) = 9 (1/3) cm = 28/3 cm
Formula used:
Volume of hollow sphere = (4/3)π(r23 - r13)
Volume of cylinder = πr2h
Curved surface area of cylinder = 2πrh
Calculation:
Volume of hollow spherical shell:
Vs = (4/3)π(83 - 43)
⇒ (4/3)π(512 - 64) = (4/3)π(448)
Vs = (1792/3)π cm3
Volume of cylinder = Volume of hollow sphere:
⇒ πr2h = (1792/3)π = r2(28/3) = 1792/3
⇒ r2 = 1792 / 28 = 64
⇒ r = 8 cm
Curved surface area of cylinder = 2πrh
⇒ 2π(8)(28/3)
CSA = 448π/3 cm2
The curved surface area of the cylinder is \(\frac{448}{3}\)π cm2.
Last updated on Apr 24, 2025
-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.
-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.
-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.
-> Eligible candidates can apply from 4th February 2025 to 5th March 2025.
-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.
-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.
-> Prepare for the exam with AAI Junior Assistant Previous year papers.