Question

A metallic ball has a radius of 9.0 cm at 0° C. Calculate the change in its volume, when it is heated to 90° C. Given that: coefficient of linear expansion of metal ball is 1.2 105 K-¹.

Answer 1

Answer:

Refer to this attachment for your answer

Answer 2

Solution:

let V be the initial volume of the ball.

ΔV be the change in volume of the ball.

T be the initial temperature of the ball.

ΔT be the change in temperature of the ball.

β be the coefficient of linear expansion of metal ball.

R be the radius of the ball.

here, given in the question that

R = 9 cm = 0.09 m

β = 1.2 105 K^-1

initial temperature, T = 0°C

final temperature = 90°C

ΔT = 90-0 = 90K

now, we know

ΔV = βVΔT

ΔV = β4/3πR^3ΔT

ΔV = 1.2105*4/3*3.14*(0.09)^3*90

ΔV = 0.333 m^3

therefore, change in the volume is 0.333 m^3