## 28. Math Puzzle $9 / 67$

At the corner of the house, there is a niche-shaped cutout from which a figure was removed during renovation. The niche has the shape of a quarter cylinder with an attached eighth sphere (height: $2 \mathrm{~m}$, radius: $1 \mathrm{~m}$) and is to be replastered.

How much mortar needs to be mixed if $22 \mathrm{~kg}$ are required on average for $1 \mathrm{~m}^{2}$ of surface area?
The following areas are to be calculated:

1. Base area of the niche: $A_{1}=\frac{\pi}{4} r^{2} \approx 0.785 \mathrm{~m}^{2}$
2. Lateral surface area of the quarter cylinder: $A_{2}=\frac{2 \pi}{4} r^{2} h \approx 1.57 \mathrm{~m}^{2}$
3. Surface area of the eighth sphere: $A_{3}=\frac{4 \pi}{8} r^{2} \approx 1.57 \mathrm{~m}^{2}$

Adding these together, the new area to be plastered is $A_{\text {Total }}=3.925 \mathrm{~m}^{2}$. Since $22 \mathrm{~kg}$ of mortar is required per $\mathrm{m}^{2}$, one needs $86.35 \mathrm{~kg} \approx 87 \mathrm{~kg}$ for the specified niche.