Question

The three metallic spheres of radius 6 cm, 8 cm and 10 cm respectively are melted to form a single solid
sphere, then the radius of the resulting sphere is
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm​

Answer 1

Answer:

c) 12 cm

Step-by-step explanation:

So lets start by finding the volumes of each sphere

Volume of sphere with radius 6 cm = x

Volume of sphere with radius 8 cm = y

Volume of sphere with radius 10 cm = z

x = (4÷3) × pi × r³

= (4÷3) × pi × (6 cm)³

= (4÷3) × pi × 216 cm³

= 905 cm³

y = (4÷3) × pi × r³

= (4÷3) × pi × (8 cm)³

= (4÷3) × pi × 512 cm³

= 2145 cm³

z = (4÷3) × pi × r³

= (4÷3) × pi × (10 cm)³

= (4÷3) × pi × 1000 cm³

= 4189 cm³

Add all of these volumes

= x + y + z

= 905 cm³ + 2145 cm³ + 4189 cm³

= 7238 cm³

This is the volume of the single solid

Volume of single solid = (4÷3) × pi × r³

7238 cm³ = (4÷3) × pi × r³

r³ = [(3÷4) × 7238 cm³] ÷ pi

r³ = 1728 cm³

r = (1728 cm³)⅓...cube root

r = 12 cm