Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+3 votes
98.8k views
in Mathematics by (53.9k points)
closed by

A Solid metallic cylinder of radius 3.5 cm and height 14 cm is melted and recast into a number of small solid metallic balls, each of radius 7/12 cm. find the number of balls so formed.

2 Answers

+1 vote
by (15.0k points)
selected by
 
Best answer

Radius of cylinder, r = 3.5 cm

Height, h = 14cm

Volume of cylinder,

V = πr2h

= π x (3.5)2 x 14

= 171.5 π

Radius of the ball, r = \(\frac 7{12}\) cm

Volume of sphere,

V \(= \frac 43 \pi r^3\)

\(= \frac 43 \pi \times \left(\frac 7{12}\right)^3\)

\(= \frac{343}{1296} \pi \)

\(= 0.2646π\)

Number of balls made,

\(n = \frac{\text{Volume of cylinder}}{\text{Volume of sphere}}\)

\(= \frac{171.5 \pi}{0.2646 \pi}\)

\(= 648.148\)

Hence, the total number of metallic balls that can be formed is 648.

+4 votes
by (65.2k points)

Let the number of recasted balls be N

Radius of cylinder R = 3.5 cm

Height of cylinder h =14 cm

Radius of recasted balls r = 7/12 cm

Volume of balls = volume of cylinder

Hence, number of recasted balls = 648

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...