Question

How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm?

Answer 1

Given :

• Radius of a sphere = 8 cm
• Radius of lead ball = 1 cm

To find :

• Number of lead balls, each of radius 1 cm which can be made from a sphere of radius 8 cm

Knowledge required :-

→ Formula of volume of sphere :-

• Volume of sphere = 4/3 πr³

where,

• Take π = 22/7
• r = radius of the sphere

Solution :

Volume of lead ball :-

⠀⠀⠀⇒ Volume = 4/3 πr³

⠀⠀⠀⇒ Volume = 4/3 π (1)³

⠀⠀⠀⇒ Volume = 4/3π

Volume of lead ball = 4/3π cm³

Volume of the sphere :-

⠀⠀⠀⇒ Volume = 4/3πr³

⠀⠀⠀⇒ Volume = 4/3π(8)³

⠀⠀⠀⇒ Volume = 4/3π × 512

Volume of the sphere = 4/3π × 512 cm³

Number of lead balls which can be made by a sphere of radius 8 cm = Volume of the speher ÷ Volume of lead ball

⠀⠀⠀⇒ Number of lead balls = $\sf{ \dfrac{ {\dfrac{ \not{4 \not\pi \times 512}}{ \not{3}} }}{ {\dfrac{ \not{4 \not\pi}}{ \not3}}}}$

⠀⠀⠀⇒ $\sf{ \dfrac{512}{1}}$

⠀⠀⠀⇒ 512

$\red\bigstar \: \: \underline{ \pmb{number \: \: of \: \: balls \: \: which \: \: can \: \: be \: \: made \: from \: a \: \: sphere \: \: of \: \: radius \: 8 \: cm \: = \purple{512}}}$

Answer 2

❥AnswEr

Given sphere,

radius=8 cm

V1 Volume of the sphere

= 34 πr3=34 π(8) 3

= 32048 πcu.cm

In the given ball

radius = 1 cm.

V2 Volume of the ball

= 34πr3= 34π(1)3

=34πcu.cm

• →Number of balls V1
• →512 Balls

hope it's helpful to you dear !!

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