Question

A 6 cm diameter spherical ball is melted and is recast into 3 smaller balls. The radius of two of the spherical balls is 1.5 cm and 2 cm. The radius of the third balls is

Answer 1

Given :

• A 6 cm diameter spherical ball is melted into 3  smaller balls.
• Radius of two of the spherical balls are 1.5 cm and 2 cm.

To find :

• Radius of third ball

Solution :

Let the radius of 3rd ball be x cm.

Diameter of big spherical ball = 6 cm

∵ Diameter = 2 × radius

∴ Radius of big ball = 6/2 = 3 cm

Volume of spherical ball is given by,

Volume (spherical ball) = 4/3 πr³

Now as the big ball is melted into 3 smaller balls, so according to question,

Volume(big ball) = Volume(1st ball) + Volume(2nd ball) + Volume(3rd ball)

⇒ 4/3 π(3)³ = 4/3 π(1.5)³ + 4/3 π(2)³ + 4/3 π(x)³

⇒ 4/3 π × 27 = 4/3 π(3.375 + 8 + x³)

⇒ 27 = 11.375 + x³                        [Cancelling 4/3 π from both sides]

⇒ x³ = 27 - 11.375

⇒ x³ = 15.625

⇒ x = ∛15.625

⇒ x = 2.5 cm

∴ Radius of third ball = 2.5 cm .

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question:- \: \star}}}}}$

A 6 cm diameter spherical ball is melted and is recast into 3 smaller balls. The radius of two of the spherical balls is 1.5 cm and 2 cm. The radius of the third balls is.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$:\implies \underline{ \boxed{ \sf r = 2.5\: cm }}\: \: \: \: \Bigg\lgroup\textsf{\textbf{Radius of the Third Ball}}\Bigg\rgroup$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

✦ A ball is melted of 6 cm diameter

✦ Now it recast into 3 smaller balls

✦ Radius of two spherical balls are 1.5 and 2 cm respectively.

Have to Find :-

Radius of the third ball.

$\Large{\underline{\underline{\bf{Solutions:-}}}}$

➹Let the Radius of the third ball be r3

➹Radius of the spherical ball R = 3 cm

➹Radius of the first ballr1 = 1.5 cm

➹Radius of the second ball, r2 = 2 cm

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･

As we know ,

$\large{\boxed{\tt{Volume_{spherical ball}\:=\:\dfrac{4}{3}\:\pi\:r^3\:}}}$

As we all know that volume will remain same it just divided into 3 parts.

Now ,  

Volume of the spherical ball = The volume of the 3 small spherical balls.

As according to the given :-

4/3πR³ = 4/3πr1³ + 4/3πr2³ + 4/3πr3³

4/3πR³ = 4/3π (r1³ + r2³ + r3³)

R³ = (r1³ + r2³ + r3³)

3³ = (1.5³ + 2³ + r3³)

27 = 3.375 + 8 + r3³

27 = 11.375 + r3³

r3³ = 27 - 11.375

r3³ = 15.625

r3 = ³√15.625

r3 = ³√ 2.5 × 2.5 × 2.5

$\sf{{2.5cm=r}}$

$\sf\bigstar\:\underline{\purple{\:\:\: Radius \: of \: the \: ball \: :-\:\:\:}}$ 2.5cm

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *