Question

0.6A solid sphere of radius 6cm is melted and then cast into small spherical balls eac
1.2cm. Find the number of balls obtained
a)500
b)1000 c)1250 d) 1500
​

Answer 1

Complete Question :-

• A solid sphere of radius 6cm is melted and then cast into small spherical balls each diameter 1.2cm. Find the number of balls obtained

Given :-

• A solid sphere of radius 6cm is melted and then cast into small spherical balls each diameter 1.2cm.

To Find :-

• The number of balls obtained = ?

Solution :-

Let the number of balls obtained be n.

• Big Sphere :-

Radius of big sphere (r) = 6 cm

→ Volume of big sphere = 4/3 πr³

→ Volume of big sphere = 4/3 × 3.14 × 6 × 6 × 6

→ Volume of big sphere = 4 × 3.14 × 6 × 6 × 2

Also,

• Small sphere :-

Radius of small sphere (r) = Diameter ÷ 2 = 1.2 ÷ 2 = 0.6 cm

→ Volume of small sphere = 4/3πr³

→ Volume of small sphere = 4/3 × 3.14 × 0.6 × 0.6 × 0.6

→ Volume of small sphere = 4 × 3.14 × 0.6 × 0.6 × 0.2

Now,

⋗ Volume of big sphere = n × Volume of small sphere

⋗ 4 × 3.14 × 6 × 6 × 2 = n × 4 × 3.14 × 0.6 × 0.6 × 0.2

⋗ 6 × 6 × 2 = n × 0.6 × 0.6 × 0.2

⋗ 72 = n × 0.072

⋗ n = 72 ÷ 0.072

⋗ n = 1000

Therefore,number of balls obtained is B) 1000.

Answer 2

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

A solid sphere of radius 6cm is melted and then cast into small spherical balls each diameter 1.2cm. Find the number of balls obtained ?

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

$\red{\bigstar}$ No. of Balls [N]

$\huge\leadsto{\sf\purple{B) \: 1000}}$

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

❥ Radius = 6 cm

❥ Small spherical balls = 1.2 cm { Diameter }

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

❥ Number of balls

Now ,

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

❥ Here we go !!

So, First we consider no. of balls be 'n' .

As we know ,

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

As we all know that volume will remain same it just divided into small spherical balls

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧

→ Volume of big sphere = 4/3 × 3.14 × 6 × 6 × 6

→ Volume of big sphere = 4 × 3.14 × 6 × 6 × 2

Volume of the solid sphere = The volume of the small spherical balls.

As according to the given :-

Also,

Radius of small sphere

= 1.2 ÷ 2 { Radius is half of the diameter }

= 0.6 cm

➹ Volume of small sphere = 4/3πr³

➹ 4/3 × 3.14 × 0.6 × 0.6 × 0.6

➹ 4 × 3.14 × 0.6 × 0.6 × 0.2

➹ Volume of big sphere = n × Volume of small sphere

➹ 4 × 3.14 × 6 × 6 × 2 = n × 4 × 3.14 × 0.6 × 0.6 × 0.2

➹ 6 × 6 × 2 = n × 0.6 × 0.6 × 0.2

➹ 72 = n × 0.072

➹ n = 72 ÷ 0.072

$\sf\bigstar\:\underline{\purple{\:\:\: No.\: of \: the \: ball \: :-\:\:\:}}$ Option B

➹ n = 1000

$\therefore\underline{\boxed{\textsf{The n = {\textbf{1000}}}}} \qquad\qquad \bigg\lgroup\bold{No. \ of \ balls \ obtain} \bigg\rgroup$

✧･ﾟ: *✧･ﾟ:*✧･ﾟ:

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .

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