$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$

Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed. As we know the angular speed depends of the frequency $f$, so if we change the frequency, the new angular speed will be:

$$
begin{align*}
omega&=2cdotpicdot{f}\
omega&=2cdotpicdot{50text{ Hz}}\
omega&=314 frac{text{rad}}{text{s}}
end{align*}
$$

Let’s substitute this in a first equation:

$$
begin{align*}
varepsilon_{max}=100cdot{1.3text{ T}}cdot{2.5cdot{10^{-3}}text{ m}^2}cdot{314 frac{text{rad}}{text{s}}}
end{align*}
$$

The maximum generator emf will be:

$$
boxed{varepsilon_{max}=102text{ V}}
$$

$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$

Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.

Let’s express the number of loops and substitute all given:

$$
begin{align*}
N&=frac{varepsilon_{max}}{{B}cdot{A}cdotomega}\
N&=frac{95text{ V}}{1.5text{ T}cdot{5.1cdot{10^{-3}}text{ m}^2}cdot{350 frac{text{rad}}{text{s}}}}\
N&=35.5
end{align*}
$$

$$
boxed{text{The minimal number of loops is $N=36$.}}
$$

$$
begin{align}
varepsilon_{max}=Ncdot{B}cdot{A}cdotomega
end{align}
$$

Where the $N$ stands for the number of loops, $A$ stands for the area of each individual loop, $B$ represents the magnitude of the magnetic field and $omega$ is the angular speed.

Let’s express and compute the area of the coil from the first equation:

$$
begin{align*}
A&=frac{varepsilon_{max}}{Ncdot{B}cdotomega}\
A&=frac{65text{ V}}{45cdot{2text{ T}}cdot{250 frac{text{rad}}{text{s}}}}
end{align*}
$$

$$
boxed{A=2.84cdot{10^{-3}}text{ m}^2}
$$