Question

two metallic spheres of radii 6cm and 8cm are melted along with another sphere and made into a big sphere of radius 12cm. find the radius of the third sphere

Answer 1

refer to the attachment

The radius of the third sphere is approx 10cm✓✓✓

Answer 2

The radius of the third sphere is 10 cm

Step-by-step explanation:

Radius of sphere 1 = 6 cm

Volume of sphere = $\frac{4}{3}\pi r^3$

Volume of sphere 1 = $\frac{4}{3}\times \frac{22}{7} \times6^{3}$

Radius of sphere 2 = 8 cm

Volume of sphere = $\frac{4}{3}\pi r^3$

Volume of sphere 2 =$\frac{4}{3}\times \frac{22}{7} \times 8^3$

Let the radius of third sphere be r

So, Volume of third sphere = $\frac{4}{3}\pi r^3$

Now we are given that two metallic spheres of radii 6cm and 8cm are melted along with another sphere and made into a big sphere of radius 12cm.

So, $\frac{4}{3} \times \frac{22}{7} \times 6^3+\frac{4}{3} \times \frac{22}{7} \times 8^3+\frac{4}{3} \times \frac{22}{7} \times r^3 =\frac{4}{3} \times \frac{22}{7} \times 12^3$

$\frac{4}{3} \times \frac{22}{7}(6^3+8^3+r^3)=\frac{4}{3} \times \frac{22}{7} \times 12^3$

$6^3+8^3+r^3=12^3\\r^3=12^3-(6^3+8^3)\\r=\sqrt[3]{12^3-(6^3+8^3)}\\r = 10$

Hence  the radius of the third sphere is 10 cm

#Learn more :

Two metallic spheres of radii6cm and 8cm are melted along with another sphere and made into a big sphere of radius 12cm. Find the radius of thrid sphere

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