Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Mensuration: 3D

Question:

15 identical solid metallic spheres of radius 3 cm are melted to form a single solid sphere. 259.97 cm³ of the material was lost in the process. What is the surface area of the newly formed sphere?

Options:

435.96 cm²

159.63 cm²

554 cm²

616 cm²

Correct Answer:

616 cm²

Explanation:

Volume of 15 smaller spheres = 15 \(\frac{4}{3}\) \(\pi \) (3)³ = 1695.6 cm³

Given, 259.97 cm³ was lost 

Thus Volume of new sphere = 1435.63cm³ =   \(\frac{4}{3}\) \(\pi \) (r)³

 r = 7 cm

Surface area = 4 \(\pi \) r² = 616 cm²