Question : A solid copper sphere of radius 6 cm is melted and redrawn into a wire, whose radius of cross-section is 8 cm. Find the length of the wire.
Option 1: 9 cm
Option 2: 2.25 cm
Option 3: 4.5 cm
Option 4: 6 cm
New: SSC MTS Tier 1 Answer key 2024 out
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 4.5 cm
Solution : The volume of the copper sphere and the copper wire will be the same, as the sphere is melted and redrawn into the wire. The volume of a sphere $ = \frac{4}{3}\pi r^3$ The volume of a cylinder $ = \pi R^2 h$ Where $R$ is the radius of the base of the cylinder and $h$ is the height (or length) of the cylinder. Given: r = 6 cm and R = 8 cm The volume of the sphere = the volume of the cylinder. $⇒\frac{4}{3}\pi (6)^3 = \pi (8)^2 h$ $⇒h= 4.5$ Hence, the correct answer is 4.5 cm.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : A solid metallic sphere of radius 9 cm is melted and recasted into a wire of radius 2 cm. What is the length of the wire?
Option 1: 343 cm
Option 2: 152 cm
Option 3: 243 cm
Option 4: 184 cm
Question : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?
Option 1: 196 cm
Option 2: 486 cm
Option 3: 224 cm
Option 4: 384 cm
Question : A large solid cube is melted and cast into ' N ' small solid spheres, each of radius 3 cm, and ' N + 2 ' small solid cuboids, each of dimensions 4 cm × 4 cm × 6.5 cm. If the length of each side of the large solid cube is 12 cm, then find the value of 'N'. [Use $\left.\pi=\frac{22}{7}\right]$
Option 1: 8
Option 2: 5
Option 3: 7
Option 4: 6
Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 2: 13 cm
Option 3: 3 cm
Question : A metallic solid sphere has a radius of 35 cm. If it is melted to form small spheres of radius 5 cm, then how many small spheres will be obtained?
Option 1: 343
Option 2: 289
Option 3: 429
Option 4: 369
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile