Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Mensuration: 3D

Question:

Radius of a large sphere is 28 m. If it is melted to form 8 equal small solid sphere, what is the sum of total surface areas of all the 8 small solid spheres?

Options:

18728 cm2

19728 cm2

19712 cm2

20568 cm2

Correct Answer:

19712 cm2

Explanation:

Volume of large solid spheres = volume of 8 small spheres

\(\frac{4}{3}\)\(\pi \)R3 = 8 × \(\frac{4}{3}\)\(\pi \)r3

\(\frac{28×28×28}{2 × 2 × 2}\) = r3

r = 14

Total surface area of solid sphere = 4\(\pi \)r2

T.S.A. of all 8 spheres = 8 × 4 × \(\frac{22}{7}\) × 14 × 14 = 19712 cm2