Question

A spherical ball of radius 3 cm is melted and recast into three spherical balls.The radii of two of these balls are 1.5 cm and 2.5 cm.Find the radius of the third ball.​

Answer 1

PLS USE THE IMAGE

PLS MARK AS BRAINLIEST

Answer 2

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➯ Radius = 2.5 cm 

Full explanation:-

Given:

• Radius of spherical ball is 3 cm.

• Radii of new spherical balls are 1.5 cm and 2 cm.

To Find:

• Radius of third spherical ball ?

Solution :

 

• Let the radius of third spherical ball be x cm.

• If something is melted and recasted into another thing then their volumes will be equal. In short

• Volume of 1st thing = Volume of second one.

➯ Let's see here

• Volume of big spherical ball will be equal to the sum of volumes of that three small spherical balls.

As we know that

★ Volume of Sphere = 4/3πr³ ★

[ Taking big spherical ball ]

• Radius = 3 cm

• ⟹ Volume = 4/3 × π × (3)³
• ⟹ 4π/3 × 27

• Volume we got = 4π/3 × 27 cm³

[ Taking 3 small spherical balls ]

• Radius of first ball (r¹) = 1.5 cm

• For second (R) = 2 cm

• For third (x) = x cm

• Volume = 4/3 × π( sum cubes of radii)

• ⟹ Volume = 4/3 × π(1.5³ + 2³ + r³)
• ⟹ 4π/3 (3.375 + 8 + x³)
• ⟹ 4π/3 ( 11.375 + x³)

• Volume we got = 4π/3 (11.375 + x³) cm³

According to the question,

• First volume = Second volume

• ➮ 4π/3 × 27 = 4π/3 (11.375 + x³)
• ➮ 27 = 11.375 + x³
• ➮ 27 – 11.375 = x³
• ➮ 15.625 = x³
• ➮ 15625/1000 = x³
• ➮ 3125/200 = 625/40 = 125/8 = x³
• ➮ ³√125/8 = x³
• ➮ 5/2 = x²
• ➮ 2.5 cm = x

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

 

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