If 3 small spherical balls having radius 3 cm, 4 cm, and 5 cm melt together to form a big spherical ball. What is the radius of big spherical ball?

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RRB NTPC Exam 19 Jan 2021 click here to view all questions

If 3 small spherical balls having radius 3 cm, 4 cm, and 5 cm melt together to form a big spherical ball. What is the radius of big spherical ball?

A8 cm

B7 cm

C6 cm

D9 cm

Akhilesh ? Apr 17 '25 at 20:46

correct answer is: option c (6 cm)
Explanation:

\( V = \frac{4}{3}\pi r^3 \)

**Steps:**

1. Calculate the volume of each small sphere:

   \( V_1 = \frac{4}{3}\pi (3)^3 = 36\pi \) cm³
   \( V_2 = \frac{4}{3}\pi (4)^3 = \frac{256}{3}\pi \) cm³
   \( V_3 = \frac{4}{3}\pi (5)^3 = \frac{500}{3}\pi \) cm³

2. Add the volumes together:

   \( V_{\text{total}} = 36\pi + \frac{256}{3}\pi + \frac{500}{3}\pi = 288\pi \) cm³

3. Solve for the radius \( R \) of the big sphere:

   \( \frac{4}{3}\pi R^3 = 288\pi \)
   \( R^3 = 216 \)
   \( R = \sqrt[3]{216} = 6 \) cm

Final Answer: \(\boxed{6 \text{ cm}}\)

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correct answer is: option c (6 cm) Explanation: \( V = \frac{4}{3}\pi r^3 \) **Steps:** Calculate the volume of each small sphere: \( V_1 = \frac{4}{3}\pi (3)^3 = 36\pi \) cm³ \( V_2 = \frac{4}{3}\pi (4)^3 = \frac{256}{3}\pi \) cm³ \( V_3 = \frac{4}{3}\pi (5)^3 = \frac{500}{3}\pi \) cm³ Add the volumes together: \( V_{\text{total}} = 36\pi + \frac{256}{3}\pi + \frac{500}{3}\pi = 288\pi \) cm³ Solve for the radius \( R \) of the big sphere: \( \frac{4}{3}\pi R^3 = 288\pi \) \( R^3 = 216 \) \( R = \sqrt[3]{216} = 6 \) cm Final Answer: \(\boxed{6 \text{ cm}}\) Akhilesh ? answered Apr 17 '25 at 20:46

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