Question

what will be the radius of a sphere made by melting three spheres of radii 3cm 4cm and 5cm​

Answer 1

GivEn:

• A sphere made by melting three spheres of radii 3cm 4cm and 5cm

To find:

• Radius of the sphere?

Solution:

☯ Let radius of circle be r cm.

We know that,

★ R³ = Radius₁³ + Radius₂³ + Radius₃³

Now, Putting value,

⇒ R³ = 3³ + 4³ + 5³

⇒ R³ = 27 + 64 + 125

⇒ R³ = 216

⇒ √R³ = 6³

⇒ r = 6cm

Thus, Radius of sphere is 6 cm.

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★ More to know:

• Volume of sphere = 4/3πr²
• Surface area sphere = 4πr²
• Diameter of sphere = 2r
• Surface area (CSA) = 4πr²
• Curved surface area of cube = 4a²
• Total surface area of cube = 6a²
• Volume of cube = a³
• Curved surface area of cuboid = 2(l + b)h
• Total surface area cuboid = 2(lb + bh + hl)
• Volume of cuboid = l × b × h
• Perimeter of Square = 4 × side
• Perimeter of Circle = 2πr
• Area of Right angle triangle = 1/2bh

Answer 2

Given :- A sphere is made by melting three spheres of radii 3 cm , 4 cm and 5 cm respectively .

To Find :- Radius of the resulting sphere.

Used Concept :- If any shape / shapes are melt / combined to form a new shape . Then the volume of the resulting shape is equal to the volume of the combined shapes where the Area of the resulting shape and the combined shape / shapes are not equal .

:- Volume of a sphere is given by 4πr³/3 . Where " r = radius of the sphere ".

Solution :- Let ,

The radius of the resulting sphere = r cm

The Sphere's that are melted to form the resulting sphere be S¹ , S² , S³ .

Now , Radius of S¹ = 3 cm

Radius of S² = 4 cm

Radius of S³ = 5 cm

According to the question :-

Volume of resulting sphere = Volume of S¹ + Volume of S² + Volume of S³ .

$\frac{4}{3} \pi \: {r}^{3} = \frac{4}{3}\pi \: {3}^{3} + \frac{4}{3}\pi {4}^{3} + \frac{4}{3}\pi \: {5}^{3}$

Taking 4π/3 Common from R.H.S .

$\frac{4}{3}\pi \: {r}^{3} = \frac{4}{3}\pi( {3}^{3} + {4}^{3} + {5}^{3})$

After Cancelling 4π/3 from both sides we get ,

${r}^{3} = {3}^{3} + {4}^{3} + {5}^{3}$

${r}^{3} = 27 + 64 + 125$

${r}^{3} = 216$

$r = \sqrt[3]{216}$

$r = 6 \: cm \:$

Therefore, radius of the resulting sphere is 6cm .