Question

Question is=

Metallic Spheres of radii 6cm , 8cm & 10cm are melt to form a single solid sphere.Find radius of the resulting sphere.

the way i solved it is above can anyone tell what i did wrong as my answer comes out to be 19.342 but correct answer is 12

(All calcualation I did are correct formula is correct so what is wrone someone please help me)​

Answer 1

Answer:

Step-by-step explanation:

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

Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³

Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³

Volume of third metallic sphere (V3) = 4/3π(r3)³ = 4/3 π (10)³

Volume of single solid sphere(V)= 4/3πR³

A .T.Q

Volume of 3 metallic spheres= volume of single solid sphere

V1+V2+V3 = V

4/3 π (6)³+ 4/3 π (8)³+4/3 π (10)³= 4/3πR³

4/3π(6³+8³+10³) = 4/3 πR³

216+ 512+ 1000 = R³

1728= R³

(12×12×12) = R³

12³= R³

R= 12

Hence, the radius of the resulting sphere = 12 cm

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

Given:

Metallic spheres of radii 6cm, 8cm & 10cm are melt to form a single solid sphere.

To find:

The radius of the resulting sphere.

$\Large{\underline{\text{Explanation\::}}}$

We have,

Three spheres of radii are melted to form a single sphere;

We know that formula of the volume of sphere:

→ $\frac{4}{3} \pi r^{3}$    [cubic units]

Given radius of the all three sphere, we get;

• Radius,1= 6cm
• Radius,2= 8cm
• Radius,3= 10cm

Now,

• Volume of First sphere:

→ $\frac{4}{3} *\pi *(r1)^{3}$

→ $\frac{4}{3} *\pi *(6cm)^{3}$

→ $\frac{4}{3} *\pi *216cm^{3}$

• Volume of Second sphere:

→ $\frac{4}{3} *\pi *(r2)^{3}$

→ $\frac{4}{3} *\pi *(8cm)^{3}$

→ $\frac{4}{3} *\pi *512cm^{3}$

• Volume of Third sphere:

→ $\frac{4}{3} *\pi *(r3)^{3}$

→ $\frac{4}{3} *\pi *(10cm)^{3}$

→ $\frac{4}{3} *\pi *1000cm^{3}$

Now,

• Volume of the single solid sphere:

Let the radius be r

A/q,

⇒ $\frac{4}{3} \pi r^{3} =\frac{4}{3} \pi *216+\frac{4}{3} \pi *512+\frac{4}{3}\pi*1000$

⇒ $\frac{4}{3} \pi r^{3} =\frac{4}{3} \pi (216+512+1000)$

⇒ $\cancel{\frac{4}{3} \pi} *r^{3} =\cancel{\frac{4}{3} \pi }(216+512+1000)$

⇒ r³ = 1728

⇒ r = ³√1728

⇒ r = ³√12 × 12× 12

⇒ r = ³√(12)³

⇒ r = 12cm

Thus,

The radius of the resulting sphere is 12cm.