Ex 13.3, 2 - Metallic spheres of radii 6 cm, 8 cm and 10 cm - Ex 13.3

Ex 13.3, 2 - Chapter 13 Class 10 Surface Areas and Volumes - Part 2
Ex 13.3, 2 - Chapter 13 Class 10 Surface Areas and Volumes - Part 3 Ex 13.3, 2 - Chapter 13 Class 10 Surface Areas and Volumes - Part 4

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 2 Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere. Since 3 spheres are melted to from one new sphere. Volume of 3 old sphere = volume of new sphere Volume of 1st sphere + volume of 2nd sphere + volume of 3rd sphere = Volume of new sphere Volume of 1st sphere, Radius (r1) = 6 cm Volume of 1st sphere = 4/3 𝜋(𝑟1)3 = 4/3×𝜋×(6)^3 = 4/3×𝜋×216 Volume of 2nd sphere, Radius (r2) = 8 cm Volume of 2nd sphere = 4/3 𝜋(𝑟2)3 = 4/3×𝜋×(8)^3 = 4/3×𝜋×512 Volume of 3rd sphere, Radius (r3) = 10 cm Volume of 1st sphere = 4/3 𝜋(𝑟3)3 = 4/3×𝜋×(10)^3 = 4/3×𝜋×1000 Volume of new sphere Let Radius = r cm Volume of new sphere = 4/3 π𝑟^3 Now , Volume of new sphere = Volume of (1st + 2nd + 3rd ) spheres 4/3 𝜋𝑟3 = 4/3 𝜋×216+4/3 𝜋×512+4/3 𝜋×1000 4/3 𝜋𝑟3 = 4/3 𝜋 (216 + 512 + 1000) 4/3 𝜋𝑟3 = 4/3 𝜋 (1728) r3 = 1728 r = ∛1728 r = ∛(12×12×12) r = ∛((12)3) r = 12 cm Hence, radius of the resulting sphere = 12 cm

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.