$1'' = \dots \text{rad}$

$(a)$ How many astronomical units $(AU)$ make $1$ parsec?
$(b)$ Consider a sun-like star at a distance of $2$ parsecs. When it is seen through a telescope with $100$ magnification,what should be the angular size of the star? The Sun appears to be $(\frac{1}{2})^{\circ}$ from the Earth. Due to atmospheric fluctuations,the eye cannot resolve objects smaller than $1$ arc minute.
$(c)$ Mars has approximately half of the Earth's diameter. When it is closest to the Earth,it is at about $\frac{1}{2} AU$ from the Earth. Calculate what size it will appear when seen through the same telescope.

The distance of the Sun from the Earth is $1.496 \times 10^{11} \ m$ and the diameter of the Sun is $1.393 \times 10^9 \ m$. Find the angular diameter of the Sun in radians.

Explain accuracy and precision in measurement.

$A$ cuboidal block has dimensions $(1.5 \times 1.5 \times 1.0) \ cm$. What is the total surface area of the cuboid (in $cm^2$)?

The nearest star to our solar system is $4.29$ light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?