Sunday Afternoon Maths I

Hide answer & extension

$$8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \mbox{ minutes}$$ $$= 8\times 7\times 4\times 3\times 1 \mbox{ hours}$$ $$= 7\times 4\times 1 \mbox{ days}$$ $$= 4\times 1 \mbox{ weeks}$$ $$= 4 \mbox{ weeks}$$

Extension

Hide answer & extension

$$\frac{1}{3}\times (2L)^2\times L\sqrt{2}$$ $$=\frac{4}{3}\sqrt{2}L^3$$ $$\frac{1}{3}\times\frac{1}{2}\times 2L\times L\sqrt{3}\times \frac{2\sqrt{2}}{\sqrt{3}}L$$ $$= \frac{2}{3}\sqrt{2}L^3$$ $$\frac{4}{3}\sqrt{2}L^3:\frac{2}{3}\sqrt{2}L^3$$ $$2:1$$

Extension

Hide answer & extension

$$R = \mbox{Area of quarter circle} - \mbox{Area of semicircle} - (\mbox{Area of semicircle} - B)$$ $$R = \frac{1}{4}\pi(2r)^2 - \frac{1}{2}\pi r^2 - \left(\frac{1}{2}\pi r^2 -B\right)$$ $$R = \pi r^2 - \frac{1}{2}\pi r^2 - \frac{1}{2}\pi r^2 +B$$ $$R=0+B$$ $$R=B$$

Extension

Hide answer & extension

Extension