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
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 7
Solution : According to the question, Volume of cube = volume of N-solid spheres + Volume of (N + 2) small cuboids ⇒ $12 \times 12 \times 12 =[ N \times \frac{4}{3}\times\pi\times 3^3] + [(N + 2)(4 \times 4 \times 6.5)]$ ⇒ $1728 = 36N\pi + 104N + 208$ ⇒ $1520 = N(36 \times\frac{22}{7} + 104)$ ⇒ $1520 = \frac{1520}{7}N$ ⇒ $N = 7$ Hence, the correct answer is 7.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : A metallic solid sphere has a radius of 28 cm. If it is melted to form small spheres of radius 3.5 cm, then how many small spheres will be obtained?
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?
Question : A solid hemisphere of radius 8 cm is melted into N identical cone whose radius is 4 cm and height is 2 cm. Then, what is the value of N?
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?
Question : How many solid spherical balls each of 33 cm radius can be made out of a solid spherical ball of radius 66 cm?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile