If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is
(a)12 cm
(b)24 cm
(c)30 cm
(d)36 cm
Answers
Answer:
The Diameter of the sphere is 24 cm
Among the given options option (b) 24 cm is the correct answer.
Step-by-step explanation:
Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere.
Given :
r1 = 6cm, r2 = 8 cm, r3 = 10 cm
Volume of first metallic sphere (V1) = 4/3π(r1)³
V1 = 4/3 π (6)³
Volume of second metallic sphere (V2) = 4/3π(r2)³
V2 = 4/3 π (8)³
Volume of third metallic sphere (V3) = 4/3π(r3)³
V3 = 4/3 π (10)³
Volume of single solid sphere(V) = 4/3πR³
A .T.Q
Volume of 3 metallic spheres = volume of single solid sphere
V1 + V2 + V3 = V
4/3 π (6)³ + 4/3 π (8)³+ 4/3 π (10)³ = 4/3πR³
4/3π(6³+8³+10³) = 4/3 πR³
216 + 512 + 1000 = R³
1728 = R³
(12×12×12) = R³
12³ = R³
R = 12
Radius of the sphere = 12 cm
Diameter of the sphere = 2 × Radius = 2 × 12 = 24 cm
Hence, the Diameter of the sphere is 24 cm
HOPE THIS ANSWER WILL HELP YOU….
Answer:
R1 = 6 cm
R2 = 8 cm
R3 = 10 cm
V1 = 4/3 pi ( R1 ) ^ 3 = 4/3 pi ( 6) ^3
❇️ V1 = 4/3 pi ( 6) ^3 cm^3
V2 = 4/3 pi ( R2 ) ^3 = 4/3 pi ( 8 ) ^3
❇️ V2 = 4/3 pi ( 8 ) ^3 cm^3
V3 = 4/3 pi ( R3 ) ^3 = 4/3 pi ( 10 ) ^3
❇️ V3 = 4/3 pi ( 10 ) ^3 cm^3
Volume of single sphere, V = 4/3 pi R^3
According to the question,
V1 + V2 + V3 = V
4/3 pi ( 6) ^3 + 4/3 pi ( 8 ) ^3 + 4/3 pi ( 10 ) ^3 = 4/3 pi R^3
4/3 pi ( 216 + 512 + 1000 ) = 4/3 pi R^3
R^3 = 1728 cm
R = 12 cm
Diameter = 2R = 2 * 12 cm = 24 cm