Step-by-step explanation:
✬ 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
⟹ 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
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.
