Question

Metallic spheres of diameters 12 cm, 16 cm and 20 cm respectively, an
form a single solid sphere. Find the radius of the resulting sphere.

Answer 1

Answer:

wait giving a pic of solution

the and is 12cm......

Answer 2

The radius of the resulting sphere is 23.04 cm.

Step-by-step explanation:

Given : Metallic spheres of diameters 12 cm, 16 cm and 20 cm respectively, an  form a single solid sphere.

To find : The radius of the resulting sphere ?

Solution :

The volume of the sphere is $V=\frac{4}{3}\pi r^3$

Volume of first metallic sphere with radius r=12 cm

$V_1=\frac{4}{3}\pi (12)^3$

Volume of second metallic sphere with radius r=16 cm

$V_2=\frac{4}{3}\pi (16)^3$

Volume of third metallic sphere with radius r=20 cm

$V_3=\frac{4}{3}\pi (20)^3$

Volume of 3 metallic spheres = Volume of  resulting sphere

i.e. $V_1+V_2+V_3=V$

$\frac{4}{3}\pi (12)^3+\frac{4}{3}\pi (16)^3+\frac{4}{3}\pi (20)^3=\frac{4}{3}\pi r^3$

$\frac{4}{3}\pi [(12)^3+(16)^3+(20)^3]=\frac{4}{3}\pi r^3$

$144+4096+8000=r^3$

$12240=r^3$

$r=\sqrt[3]{12240}$

$r=23.04$

Therefore, the radius of the resulting sphere is 23.04 cm.

#Learn more

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted

to form a single solid sphere. Find the radius of the resulting sphere.

https://brainly.in/question/1205