Question

$\Large{\underline{\underline{\bf{\red{Question:-}}}}}$
✧ 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.

Don't spam ✘
Need quality answer ✔​

Answer 1

✬ Radius = 2.5 cm ✬

Step-by-step 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

$\implies{\rm }$ Volume = 4/3 × π × (3)³

$\implies{\rm }$ 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)

$\implies{\rm }$ Volume = 4/3 × π(1.5³ + 2³ + r³)

$\implies{\rm }$ 4π/3 (3.375 + 8 + x³)

$\implies{\rm }$ 4π/3 ( 11.375 + x³)

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

A/q

• 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.

Answer 2

Answer:

Volume of spherical box =

$\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3 = {792}^{3}$

Total volume of the two smaller balls of radii 1.5 cm and 2 cm

$\frac{4}{3} \times \frac{22}{7} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} + \frac{4}{3} - \frac{22}{7} \times 2 \times 2 \times 2$

[Therefore , V = 4/3 πr³]

Volume of third ball =

$\frac{792} {7} - \frac{143}{3} = \frac{2376 - 1001}{21}$

Let r be the radius of third ball

$\frac{4}{3} \times \frac{22}{7} \times {r}^{3} = \frac{1375}{21}$

${r}^{3} = \frac{1375}{21} \times \frac{3}{4} \times \frac{7}{2}$

${r}^{3} = \frac{125}{8}$

Therefore Radius =

$3 \sqrt{ \frac{125}{8} }$

$= 2 \times \frac{5}{2}$

Diameter = 5

$radius \: = \frac{5}{2} = 2 \frac{1}{2} or \: 2.5$

How was it tell in comment