Category: Geometry

Question Number 5543 by Rasheed Soomro last updated on 19/May/16 $$\bullet \mathrm{What}\mathbf{plane}\mathbf{geometrical}\mathbf{figures}$$$$\mathrm{could}\mathrm{be}\mathrm{produced}\mathrm{by}\mathrm{joining}$$$$\mathbf{vertices}\mathbf{of}\mathbf{a}\mathbf{cube}?$$$$(\mathrm{for}\mathrm{example}:\mathrm{square})$$$$\bullet \mathrm{What}\mathrm{largest}\mathrm{area}\left(2\mathrm{dimensional}\right)\mathrm{can}\mathrm{be}\mathrm{obtained}$$$$\mathrm{by}\mathrm{joining}\mathrm{vertices}\mathrm{of}\mathrm{a}\mathrm{cube}\mathrm{when}\mathrm{its}\mathrm{side}\mathrm{is}\mathrm{x}?$$ Terms of…

Question Number 5533 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Measure}\mathrm{of}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{cube}\mathrm{is}\mathrm{double}$$$$\mathrm{of}\mathrm{the}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{cube}\mathrm{inside}\mathrm{it}.$$$$\mathrm{What}\mathrm{is}\mathrm{empty}\mathrm{space}\mathrm{in}\mathrm{larger}\mathrm{cube}?$$ Commented by FilupSmith last updated on 18/May/16 $$\mathrm{Empty}\:\mathrm{space}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{larger}…

Question Number 5529 by Rasheed Soomro last updated on 18/May/16 Commented by Rasheed Soomro last updated on 18/May/16 $$△\mathrm{ABC}\mathrm{is}\mathrm{an}\mathrm{equilaterl}\mathrm{triangle}.$$$$\mathrm{D},\mathrm{E},\mathrm{F}\mathrm{are}\mathrm{mid}-\mathrm{points}\mathrm{of}\mathrm{the}\mathrm{sides}.$$$$\mathrm{The}\mathrm{centres}\mathrm{of}\mathrm{arcs}\mathrm{are}\mathrm{vertices}\mathrm{of}$$$$\bigtriangleup\mathrm{ABC}.…

Question Number 5515 by FilupSmith last updated on 17/May/16 $$\mathrm{If}\mathrm{you}\mathrm{have}\mathrm{a}\mathrm{regular}n-\mathrm{sided}\mathrm{polygon},$$$$\mathrm{is}\mathrm{there}\mathrm{a}\mathrm{method}\mathrm{to}\mathrm{calculate}\mathrm{the}\mathrm{area}$$$$\mathrm{from}\mathrm{one}\mathrm{corner}\mathrm{to}\mathrm{another}?$$$$$$$$\mathrm{That}\mathrm{is},\mathrm{if}\mathrm{we}\mathrm{start}\mathrm{at}\mathrm{a}\mathrm{corner}\left(\mathrm{corner}1\right),$$$$\mathrm{and}\mathrm{draw}\mathrm{a}\mathrm{line}\mathrm{to}\mathrm{corner}x,\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{area}?$$$$\mathrm{See}\mathrm{image}\mathrm{in}\mathrm{comment}\mathrm{for}\mathrm{visual}\mathrm{representation}.$$ Commented…

Question Number 5490 by 123456 last updated on 16/May/16 $$\int \sqrt{r^2-x^2}dx=?$$$$\underset{-r}{\stackrel{x}{\int }}\sqrt{r^2-x^2}dx=??$$$$\underset{{x}} {\overset{{y}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=??? \…