Question : A solid metallic sphere of radius 13 cm is melted and recast into a cone having a diameter of the base as 13 cm. What is the height of the cone?
Option 1: 246 cm
Option 2: 152 cm
Option 3: 174 cm
Option 4: 208 cm
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 208 cm
Solution :
We know,
The volume of a cone = $\frac{1}{3}πr^2h$, where r is the radius of the cone
The volume of a sphere = $\frac{4}{3}πR^3$, where r is the radius of the sphere
According to the question,
$\frac{4}{3}πR^3 = \frac13πr^2h$
Let the height of the cone be h
⇒$\frac{4}{3}π(13)^3 = \frac13π(\frac{13}{2})^2h$
⇒ $h = 4 × 13^3 × (\frac{2}{13})^2$
⇒ $h = 16 × 13$
⇒ $h = 208$ cm
⇒ Height of the cone = 208 cm
Hence, the correct answer is 208 cm.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
