A glass has a circlar base with a radius of 3.5 cm. A rectangular tray has dimensions 40 cm by 25cm. how many glasses will fit the tray?

First, we find the area of the base of the glasses, so using pi r^2, the area is $${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{3.5}}}^{{\mathtt{2}}} = {\mathtt{38.484\: \!510\: \!006\: \!474\: \!967\: \!2}}$$cm2

next, find the area of the tray, so $${\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{25}}$$=1000cm2. Divide the area of the tray by the area of the glass to get your answer.

$${\frac{{\mathtt{1\,000}}}{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}\left({{\mathtt{3.5}}}^{{\mathtt{2}}}\right)\right)}} = {\mathtt{25.984\: \!480\: \!504\: \!799\: \!238\: \!5}}$$

so 25.9844805047992385 glasses or 25 whole glasses (we must round down in this case, otherwise, we go over the tray area)