Question

Metallic spheres of radius 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. Find the radius of resulting sphere​

Answer 1

Answer:

12cm

Step-by-step explanation:

vol of 1st sphere = 4/3pie6³

vol of 2nd sphere = 4/3pie8³

vol. of 3d sphere= 4/3pie10³

vol of new sphere = 4/3pieR³= 4/3pie(6³+8³+10³)

4/3pieR³ = 4/3pie1728

R³= 1728

R=12cm

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

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