Question

two metallic spheres of the radius 6 CM and 8cm and big sphere of radius 12cm find the radius of third sphere
​

Answer 1

Answer:

12 cm

Step-by-step explanation:

Radius (1) of 1st sphere = 6 cm

Radius (12) of 2nd sphere 8 cm

Radius (13) of 3rd sphere = 10 cm

Let the radius of the resulting sphere be r.

The object formed by recasting these spheres will

be the same in volume as the sum of the volumes

of these spheres.

The volume of 3 spheres = Volume of resulting

sphere

4/3 π [ r1³+ r2³+ r3³ - 4/3 π r³

4/3 π [ 6³+8³+10³] = 4/3 π r³

r³ = 216 + 512 + 1000

r³ = 1728

r³ = 12 cm

Answer 2

↦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.

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★ 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