Question : A solid metallic sphere of radius 8.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height of the cylinder? (Your answer should be correct to one decimal place.)

Option 1: 6.5 cm

Option 2: 5.5 cm

Option 3: 7.0 cm

Option 4: 6.0 cm


Team Careers360 7th Jan, 2024
Answer (1)
Team Careers360 9th Jan, 2024

Correct Answer: 5.5 cm


Solution : Given: Radius of sphere $r$ = 8.4 cm
The radius of cylinder $R$ = 12 cm
Let the height of the cylinder be $h$ cm.
According to the question,
The volume of the cylinder = volume of the sphere
$\pi R^2h = \frac{4}{3}\pi r^3$
⇒ $12 \times 12 \times h = \frac{4}{3} \times 8.4 \times 8.4 \times 8.4$
⇒ $h = \frac{4 \times 8.4 \times 8.4 \times 8.4}{3 \times 12 \times 12}$
⇒ $h = 5.488= 5.5$ (correct to one decimal place)
Hence, the correct answer is 5.5 cm.

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