Alan

Snell's law says that:  sin(θ₁)/sin(θ₂) = n₂/n₁ where the n's are the indices of refraction.  If the angle of incidence is zero, then the angle of refraction will be zero also, as the angles refer to the deviation from the normal to the surface.  However, I guess in your case you mean the angle from the surface, so that you are talking about grazing incidence.  In this case θ₁ is actually 90° and sin(θ₂) =  sin(90°)*1/1.5 = 1/1.5 so

$${\mathtt{theta2}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{1.5}}}}\right)} \Rightarrow {\mathtt{theta2}} = {\mathtt{41.810\: \!314\: \!895\: \!779^{\circ}}}$$

or θ₂ ≈ 41.81° (Note that this is also the angle made with the normal to the surface.  The angle made with the surface will be 90° - 41.81°.)

Because of the positioning of the 2's and the 1/2 on the outside, it looks to me as if the following is what is wanted:

$${\left[{\mathtt{0.05}}{\mathtt{\,\times\,}}{\left({\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\left({\mathtt{\,-\,}}{\mathtt{22}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\left({\mathtt{12}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\left({\mathtt{14}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.05}}{\mathtt{\,\times\,}}{\left({\mathtt{28}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}\right]}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\mathtt{16.976\: \!159\: \!754\: \!196\: \!471\: \!4}}$$

or, ≈ $16.98

(I copied and pasted rather than rewriting this, then inserted ^ and * as appropriate and changed the long horizontal lines to - signs.)

Since 6³ is greater than 201, but 5³ is less than 201 there must be 201 - 5 or 196 integers that are not perfect cubes.

Yet again, look at

Again, look at 

Look at the two I've done here: 

Look at it this way:

Let        x = 0.9999999999.....

Then  10x = 9.9999999999...

Subtract the first from the second to get

10x - x = 9.999999999.... - 0.999999999...  

or 9x = 9

so x = 1

The area of a full circle is pi*radius², so the area of a semicircle is (1/2)pi*radius².

$$\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{7.89}}}^{{\mathtt{2}}} = {\mathtt{97.785\: \!370\: \!015\: \!268\: \!583\: \!8}}$$

area ≈ 97.79 cm²