Question

three spheres of radii 2cm, 3cm,4cm are melted together to form a single sphere.find the radius of new sphere.​

Answer 1

Answer:

$\bigstar{\bold{Radius=4.63\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Radius of first sphere(r₁)  = 2 cm
• Radius of second sphere (r₂) = 3 cm
• Radius of third sphere (r₃) = 4 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Radius of new sphere formed (R)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Volume of new sphere = Volume of first sphere + Volume of second sphere +  Volume of third sphere

Volume of first sphere:

Volume of sphere = 4/3 × π × (r₁)³

→ Substitute the datas

  Volume of sphere = 4/3 × 3.14 × 2³

  Volume of first sphere = 33.5 cm³

Volume of second sphere:

Volume of sphere = 4/3 × π × (r₂)³

→ Substitue the datas,

  Volume of second sphere = 4/3 × 3.14 × 3 × 3 ×3

  Volume of second sphere = 113.04 cm³

Volume of third sphere:

Volume of sphere = 4/3 × π × (r₃)³

→ Substitute the datas,

  Volume of third sphere = 4/3 × 3.14 × 4 × 4 ×4

  Volume of third sphere = 268 cm³

→ Volume of new sphere = 33.5 + 113.04 + 268

   Volume of new sphere = 414.54 cm³

   4/3 × 3.14 × R³ = 414.54

   4/3 ×  R³ = 132

    R³ = 132 × 3/4

    R³ = 99

   R = ∛99

   R = 4.63 cm

$\boxed{\bold{Radius=4.63\:cm}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Volume of a shere is given by the formula ,

  Volume = 4/3 × π × r³