Three spheres are made by melting a solid metallic sphere of radius 6

1.	Three spheres are made by melting a solid metallic sphere of radius 6 cm. If the radii of the two spheres are 3 cm and 4 cm respectively, then the radius of the third spheres is ………………… cm.A) 5 B) 2 C) 4 D) 3
Answer» Correct option is: A) 5 Let the radius of third sphere be r cm. \(\because\) Three spheres of radii 3 cm, 4 cm and r cm are made by melting a solid metallic sphere of radius 6 cm. \(\therefore\) Volume of sphere of 6 cm radius = Combined volume of formed three spheres \(\Rightarrow\) \(\frac 43 \pi \times 6^3 = \frac 43 \pi \times 3^3 + \frac 43 \pi \times 4^3 + \frac 43 \pi r^3 \) \(\Rightarrow\) \(6^3 = 3^3 + 4^3 +r^3\) = \(r^3 = 6^3 - 3^3 - 4^3 = 216 - 27 - 64\) = 216 - 91 = 125 = \(5^3\) = r = 5 cm Hence, the radius of the third sphere is 5 cm. Correct option is: A) 5

Three spheres are made by melting a solid metallic sphere of radius 6 cm. If the radii of the two spheres are 3 cm and 4 cm respectively, then the radius of the third spheres is ………………… cm.A) 5 B) 2 C) 4 D) 3

Answer»

Correct option is: A) 5

Let the radius of third sphere be r cm.

\(\because\) Three spheres of radii 3 cm, 4 cm and r cm are made by melting a solid metallic sphere of radius 6 cm.

\(\therefore\) Volume of sphere of 6 cm radius = Combined volume of formed three spheres

\(\Rightarrow\) \(\frac 43 \pi \times 6^3 = \frac 43 \pi \times 3^3 + \frac 43 \pi \times 4^3 + \frac 43 \pi r^3 \)

\(\Rightarrow\) \(6^3 = 3^3 + 4^3 +r^3\)

= \(r^3 = 6^3 - 3^3 - 4^3 = 216 - 27 - 64\)

= 216 - 91 = 125 = \(5^3\)

= r = 5 cm

Hence, the radius of the third sphere is 5 cm.

Correct option is: A) 5