Question : An inverted conical–shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and the radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius $\frac{1}{2}$ cm are dropped in the vessel, 25% water is overflowed. The number of balls is:

Option 1: 100

Option 2: 400

Option 3: 200

Option 4: 150


Team Careers360 19th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

Correct Answer: 100


Solution : Given: Height of the vessel = 8 cm
Radius = 5 cm.
Volume of the conical vessel = $\frac{1}{3}\pi r^2 h$
= $\frac{1}{3}\times \pi\times 5^2\times 8$
= $\frac{200}{3}\pi$ cm$^3$
The volume of 25% of water = $\frac{1}{4}\times\frac{200}{3}\pi=\frac{50}{3}\pi$ cm$^3$
The volume of the spherical metallic ball of the radius $R = \frac{4}{3} \pi R^3$
$=\frac{4}{3}\times \pi\times (\frac{1}{2})^3=\frac{\pi}{6}$ cm$^3$
The number of balls required = $\frac{\frac{50}{3}\pi}{\frac{\pi}{6}}$ = 100
Hence, the correct answer is 100.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books