metallic sphere of radius 6cm 8cm and 10cm respectively are melted and recast into a single solid sphere find the surface area of solid sphere formed
Answers
Answer:
1808.64cm²
Step-by-step explanation:
4/3π [r1³+r2³+r3³] =4/3πR³
4/3 and π cancel
6³+8³+10³= R³
216+512+1000=R³
1728=R³
R=12cm
surface area= 4πr²
taking π=3.14
4×314×12×12/100
⇒1808.64cm²
Answer:
1808.64 cm²
Step-by-step explanation:
r₁ = 6 cm
r₂ = 8cm
r₃ = 10cm
Let the radius of the new sphere formed be R and its volume of V
The volume of a sphere = 4/3 πr³
Since the spheres are melted and recast into a single solid sphere,
Volume of the new sphere = Sum of the volume of the three spheres
V = V₁ + V₂ + V₃
4/3 π R³ = 4/3 πr₁³ + 4/3π r₂³ +4/3 r₃³
R³ = r₁³ + r₂³ + r₃³
R³ = 6³ + 8³ + 10³
R³ = 216 + 512 + 1000
R³ = 1728
R = 12cm
Surface area of a sphere = 4 π r²
= 4 × 3.14 × 12²
=1808.64 cm²