Question

Three metallic spheres of radii 6cm,8cm,10cm respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.​

Answer 1

Question =》

Three metallic spheres of radii 6cm,8cm,10cm respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.

Given =》

r1=6cm, r2=8cm, r3=10cm

Let r1,r2,r3 be the radius of the given three spheres ans R be the radius of single solid sphere .2

Solution =》

Volume of first metallic sphere (v1)=4/3π(r1)³

=4/3π6³

Volume of second metallic sphere (v2)=4/3π(r2)³

=4/3π8³

Volume of third metallic sphere (v3)=4/3π(r3)³

=4/3π10³

=4/3pi R³

A to Q,

Volume of 3 metallic spheres= volume of single solid sphere

V1+V2+V3=V

4/3π(6³)+4/3π(8³)+4/3π(10³)=4/3πR³

=4/3π(6³+8³+10³)=4/3πR³

=216+512+1000=R³

=1728=R³

12×12×12=R³

12³=R³

R=12

Hence, the radius of resulting sphere=12cm

Answer 2

Step-by-step explanation:

↦Firstly let's understand the concept used

Here the concept of Volume of Spheres has been used. We see that we are given the values of radii of three spheres. If we add the volume of all these spheres, we can get the volume of the resulting sphere which if formed by melting these initial spheres. This is volume can neither be destroyed nor be created because its amount of matter. Let's do it !!

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★ Formula Used :-

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

Volume of the resulting Sphere = Volume of Sphere

(radius 6cm+8cm+10cm)

$\frac{4}{3} \pi {}( 6+ 8 + 10)^{3}$

$\frac{4}{3} \pi {r}^{3}$

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★ Question :-

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a

single solid sphere. Find the diameter of the resulting sphere.

____________________________________

★ Solution :-

Given,

» Radii of metallic sphere = 6 cm

» Radii of metallic sphere = 8 cm

» Radii of metallic sphere = 10 cm

Then according to the question :-

~ For the volume of sphere with radius 6 cm :-

$⟶Volume \: of \: Sphere= \frac{4}{3} \pi {r}^{3}$

$⟶VolumeofSphere </p><p>(r=6cm)</p><p> \frac{4}{3} \times \frac{22}{7} \times {6}^{3}$

$\frac{19008}{21}$

~ For the volume of sphere with radius 8 cm :-

$⟶VolumeofSphere= \frac{4}{3} \pi {r}^{3}$

$⟶VolumeofSphere </p><p>(r=8cm) \: \frac{4}{3} \times \frac{22}{7} \times {8}^{3}$

$\frac{45056}{21}$

~ For the volume of sphere with radius 10 cm :-

$⟶VolumeofSphere= \frac{4}{3} \pi {r}^{3}$

$⟶VolumeofSphere </p><p>(r=10cm) \frac{4}{3} \times \frac{22}{7} \times {10}^{3} </p><p>$

$\frac{88000}{21}$

~ For the radius of Resulting Sphere :-

• Let the radius of resulting sphere be r' cm. Then,

$\frac{19008}{21} + \frac{45056}{21} + \frac{88000}{21}$

$\frac{⟶ </p><p>21</p><p>19008+45056+88000}{21}$

$\frac{152064}{21}$

Volume of metallic sphere:-

$\frac{4}{3} \times \frac{22}{7} \times \frac{152064} {21} ^{3}$

${r}^{3} = 1728 \: {cm}^{3}$

= 12cm

VolumeofSphere

(resulting)

=12cm

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★ More to know :-

• Volume of Cylinder = πr²h

• Volume of Cube = (Side)³

• Volume of Cone = ⅓ × πr²h

• Volume of Hemisphere = ⅔ × πr³