On what does the proportionality constant depend in Newton's law of cooling?

$A$ body cools in $7$ minutes from $60^{\circ}\,C$ to $40^{\circ}\,C$. The temperature of the surrounding is $10^{\circ}\,C$. The temperature of the body after the next $7$ minutes will be

$A$ sphere,a cube,and a disc,all of the same material,quality,and volume,are heated to $600\,^{\circ}C$ and left in air. Which of these will have the lowest rate of cooling?

Two spheres of radii $R_1$ and $R_2$ have densities $\rho_1$ and $\rho_2$ and specific heats $S_1$ and $S_2$. If they are heated to the same temperature,what is the ratio of their rates of cooling?

$A$ body cools in a surrounding which is at a constant temperature of $\theta_0$. Assuming that it obeys Newton's law of cooling,its temperature $\theta$ is plotted against time $t$. Tangents are drawn to the curve at the points $A(\theta = \theta_1)$ and $B(\theta = \theta_2)$. These tangents meet the time-axis at angles $\alpha_1$ and $\alpha_2$ as shown in the graph. Then:

$A$ body initially at $80^\circ C$ cools to $64^\circ C$ in $5$ minutes and to $52^\circ C$ in $10$ minutes. The temperature of the body after $15$ minutes will be ...... $^\circ C$.