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______.
Option 1: 8 cm
Option 2: 4 cm
Option 3: 6 cm
Option 4: 10 cm
New: SSC CHSL tier 1 answer key 2024 out | 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: 8 cm
Solution : Radius of sphere = 4 cm Volume of sphere = $\frac{4}{3} \pi r^3$ = $\frac{4}{3} \pi (4)^3$ Let the radius of the base of the cone be $R$ and the height is 4 cm. Now volume of cone = $\frac{1}{3} \pi r^2h$ = $\frac{1}{3} \pi R^2 \times 4$ According to the question, The volume of cone = Volume of a sphere $⇒\frac{1}{3} \pi R^2 \times 4 = \frac{4}{3} \pi (4)^3$ $⇒R^2=(4)^3 = 64$ $⇒R=8$ cm Hence, the correct answer is 8 cm.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
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 : 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 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:
Question : How many solid spherical balls of radius 6 cm can be made by melting a solid hemisphere of radius 12 cm?
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.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile