Question : A metallic sphere of radius 10 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. The number of cones thus formed is:
Option 1: 140
Option 2: 132
Option 3: 112
Option 4: 126
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
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 126
Solution : The volume of a sphere $V_{\text{s }} = \frac{4}{3} \pi r^3$ where $r$ is the radius. The volume of a cone $V_{\text{c}} = \frac{1}{3} \pi r^2 h$ where $r$ is the radius and $h$ is the height. Given that the sphere and the cones are made of the same material. Let the number of cones as $n$. $V_{\text{s}} = n \times V_{\text{c}}$ ⇒ $\frac{4}{3} \pi (10.5)^3 = n \times \frac{1}{3} \pi (3.5)^2 \times 3$ ⇒ $n = \frac{4 \times (10.5)^3}{(3.5)^2 \times 3} = 126$ Hence, the correct answer is 126.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
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.
Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Question : A solid sphere of radius 4 cm is melted and cast into the shape of a solid cone of height 4 cm. The radius of the base of the cone is______.
Question : 24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.
Question : The radius of a sphere is 3.5 cm. What is the total surface area of the sphere?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile