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Question Number 3709 by Rasheed Soomro last updated on 19/Dec/15
$$\mathcal{W}{hat}\:{is}\:{a}\:{solid}\:{angle}? \\ $$$$\mathcal{H}{ow}\:{is}\:{it}\:{defined}? \\ $$$${Does}\:{the}\:{corner}\:{of}\:{a} \\ $$$${cubic}\:{room}\:{can}\:{be}\:{said} \\ $$$$'\:{right}\:{solid}\:{angle}\:'\:? \\ $$
Answered by 123456 last updated on 20/Dec/15
$$\mathrm{a}\:\mathrm{angle}\:\left(\mathrm{radians}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{measure}\:\mathrm{of}\:\mathrm{arc} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{his}\:\mathrm{radius} \\ $$$$\theta=\frac{\overset{\frown} {{l}}}{{r}} \\ $$$$\mathrm{the}\:\mathrm{solid}\:\mathrm{angle}\:\mathrm{is}\:\mathrm{similiar}\:\mathrm{to}\:\mathrm{this},\:\mathrm{but} \\ $$$$\mathrm{instead}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of} \\ $$$$\mathrm{it} \\ $$$$\mho=\frac{{S}}{{r}^{\mathrm{2}} } \\ $$$$\mathrm{the}\:\mathrm{full}\:\mathrm{solid}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{is}\:\mathrm{4}\pi \\ $$$$\left(\mathrm{steroradians},\:\mathrm{if}\:\mathrm{im}\:\mathrm{not}\:\mathrm{wrong}\right) \\ $$
Commented by Rasheed Soomro last updated on 20/Dec/15
$$\mathcal{T}{hanks}! \\ $$$${Is}\:{S}\:{area}\:{of}\:{surface}? \\ $$$$\mathcal{W}{hat}\:{shape}\:{of}\:{surface}\:{S}\:{is}\:{taken}? \\ $$
Commented by 123456 last updated on 20/Dec/15
$$\mathrm{spherical}\::\mathrm{v} \\ $$
Commented by Rasheed Soomro last updated on 20/Dec/15
$$\mathcal{W}{hat}\:{is}\:{definition}\:{of}\:\mathrm{steroradians}? \\ $$$$\mathcal{O}{f}\:{course}\:{S}\:{is}\:\:{a}\:{portion}\:{of}\:{spherical} \\ $$$${surface}.\:{What}\:{is}\:{the}\:{shape}\:{of}\:{the}\:{portion}? \\ $$