Question : A metallic sphere of radius 21 cm is melted and then recast into smaller cones, each with a 7 cm radius and a height of 3 cm. Find the number of cones obtained.
Option 1: 225
Option 2: 325
Option 3: 522
Option 4: 252
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 252
Solution :
Let the number of cones made be $n$.
In this case, the metallic sphere is melted and then cast into smaller cones.
So, Volume of Sphere $= n\times$ Volume of cone
⇒ $\frac{4}{3}\pi r{_s}^3=n\times\frac{1}{3}\pi r{_c}^2h$ where $r_s$ is the radius of the sphere, $r_c$ is the radius of the cone, and $h$ is the height of the cone.
⇒ $4\times r{_s}^3=n\times r{_c}^2h$
⇒ $4\times (21)^3=n\times (7)^2\times 3$
⇒ $n=\frac{4\times 21\times 21\times 21}{7\times 7\times 3}$
⇒ $n=4\times3\times 21$
⇒ $n=252$
Hence, the correct answer is 252.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
