20 identical solid hemispheres of radius 3 cm are melted…

20 identical solid hemispheres of radius 3 cm are melted to form a big solid hemisphere. What is the radius (in cm) of the biggest hemisphere formed, if 20% of the solid is wasted during the process?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. $6\sqrt[3]2$ .

Volume of 1 small hemisphere(V) = $2\over3$ πr³

here, r = radius

Volume of 20 hemispheres = 20 × $2\over3$ × π × 27 = 360π

Remaining volume = $80\over100$ × 360π = 288π

Let R be the radius of the big hemisphere

⇒ $2\over3$ πR³ = 288π

⇒ R³ = 432

⇒ R = $\sqrt[3] {432}$ = $6\sqrt[3]2$

SSC MTS 2024 PYQ — Question 9