Question

$\huge \underline\bold{➟Question}$

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radius of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

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Answer 1

Answer:

2.5 cm

Step-by-step explanation:

Given

• Radius of spherical ball → 3 cm
• Spherical ball is melted and recast into three spherical ball.
• Radius of two of those spherical balls are 1.5 cm and 2 cm

To find:-

• Radius of third ball.

Solution:-

Let the radius of the unknown ball be x.

r₁ = 1.5 cm

r₂ = 2 cm

r₃ = x cm

r = 3 cm

Volume of Spherical Ball = Volume of 1st Ball + Volume of 2nd Ball + Volume of 3rd Ball

$\dashrightarrow \dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi r_1^3 +\dfrac{4}{3}\pi r_2^3 + \dfrac{4}{3}\pi r_3^3$

$\dashrightarrow \dfrac{4}{3}\pi( 3^3) = \dfrac{4}{3}\pi ( r_1^3 + r_2^3 + r_3^3 )$

$\dashrightarrow 3^3 = r_1^3 + r_2^3 + r_3^3$

$\dashrightarrow 3^3 = (1.5)^3 + (2)^3 + (x)^3$

$\dashrightarrow 27 = 3.375 + 8 + x^3$

$\dashrightarrow 27 = 11.375 + x^3$

$\dashrightarrow x^3=27-11.375$

$\dashrightarrow x^3=15.625$

$\dashrightarrow x=\sqrt[3]{15.625}$

$\bf\dashrightarrow x=2.5cm$

Hence, the radius of the spherical ball is 2.5 cm.

Answer 2

Answer :-

The radius of spherical ball = 3 cm

Volume of spherical ball = 4/3πr³

= 4/3π × 3 × 3 × 3

= 36π cm³

∵ Volume of spherical ball = Total volume of three small spherical ball

∵ The radii of the ball are 1.5 cm and 2 cm

∴ Let the radius of third ball = r

∴ Volume of spherical ball = Total volume of three small spherical balls

36π = 4/3π × (3/2)³ + 4/3π × (2)³ + 4/3 πr³

36π = 4/3π × 27/8 + 4/3π × 8 + 4/3πr³

36π = 4/3π(27/8 + 8 + r³)

(36π × 3)/4π = 27/8 + 8 + r³

27 = (27 + 64)/8 + r³

27 = 91/8 + r³

27 – 91/8 = r³

(216 – 91)/8 = r³

125/8 = r³

³√125/8 = r

r = 5/2 cm

Final answer :-

Hence, The radius of third ball is 5/2cm.