An iron ring $($illustrated below$)$ is heated from room temperature to $300C.$ Use the information beside the illustration to answer the questions that follow. Show all relevant formulae and calculations.

Dimensions at room temperature $(25C)$ :

inner radius, $r=15mm$

thickness, $t=4mm$

height, $h=8mm$

Linear coefficient of thermal expansion, ${}_l=11\mathrm{.}8{10}^{-6}{K}^{-1}$

a$)$ What is the volume of the ring at $300C?$

b$)$ What is the ratio of the volume of the ring at $300C$ to the volume of the ring at room temperature?