Cho hình nón có góc ở đỉnh bằng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOnaiaaic % dacqGHWcaScaGGSaaaaa!3A09! 60^\circ ,\) diện tích xung quanh bằng \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOnaiabec % 8aWjaadggadaahaaWcbeqaaiaaikdaaaaaaa!3A40! 6\pi {a^2}\). Tính thể tích của khối nón đã cho.
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Lời giải:
Báo saiThể tích: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2 % da9maalaaabaGaaGymaaqaaiaaiodaaaGaeqiWdaNaamOuamaaCaaa % leqabaGaaGOmaaaakiaadIgacqGH9aqpdaWcaaqaaiaaigdaaeaaca % aIZaaaaiabec8aWjaac6cacaWGpbGaamyqamaaCaaaleqabaGaaGOm % aaaakiaac6cacaWGtbGaam4taiaac6caaaa!486A! V = \frac{1}{3}\pi {R^2}h = \frac{1}{3}\pi .O{A^2}.SO.\)
Ta có: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaecaaeaaca % WGbbGaam4uaiaadkeaaiaawkWaaiabg2da9iaaiAdacaaIWaGaeyiS % aaRaeyO0H49aaecaaeaacaWGbbGaam4uaiaad+eaaiaawkWaaiabg2 % da9iaaiodacaaIWaGaeyiSaalaaa!4780! \widehat {ASB} = 60^\circ \Rightarrow \widehat {ASO} = 30^\circ \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taci % iDaiaacggacaGGUbGaaG4maiaaicdacqGHWcaScqGH9aqpdaWcaaqa % aiaad+eacaWGbbaabaGaam4uaiaad+eaaaGaeyypa0ZaaSaaaeaaca % aIXaaabaWaaOaaaeaacaaIZaaaleqaaaaakiabgkDiElaadofacaWG % pbGaeyypa0Jaam4taiaadgeadaGcaaqaaiaaiodaaSqabaGccaGGUa % aaaa!4DD0! \Rightarrow \tan 30^\circ = \frac{{OA}}{{SO}} = \frac{1}{{\sqrt 3 }} \Rightarrow SO = OA\sqrt 3 .\)
Lại có: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa % aaleaacaWG4bGaamyCaaqabaGccqGH9aqpcqaHapaCcaWGsbGaamiB % aiabg2da9iabec8aWjaac6cacaWGpbGaamyqaiaac6cacaWGtbGaam % yqaiabg2da9iabec8aWjaac6cacaWGpbGaamyqamaakaaabaGaam4t % aiaadgeadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaWGtbGaam4tam % aaCaaaleqabaGaaGOmaaaaaeqaaOGaeyypa0JaaGOnaiabec8aWjaa % dggadaahaaWcbeqaaiaaikdaaaaaaa!555D! {S_{xq}} = \pi Rl = \pi .OA.SA = \pi .OA\sqrt {O{A^2} + S{O^2}} = 6\pi {a^2}\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % 4taiaadgeadaGcaaqaaiaad+eacaWGbbWaaWbaaSqabeaacaaIYaaa % aOGaey4kaSIaaG4maiaad+eacaWGbbWaaWbaaSqabeaacaaIYaaaaa % qabaGccqGH9aqpcaaI2aGaamyyamaaCaaaleqabaGaaGOmaaaakiab % gkDiElaaikdacaWGpbGaamyqamaaCaaaleqabaGaaGOmaaaakiabg2 % da9iaaiAdacaWGHbWaaWbaaSqabeaacaaIYaaaaaaa!4D8D! \Rightarrow OA\sqrt {O{A^2} + 3O{A^2}} = 6{a^2} \Rightarrow 2O{A^2} = 6{a^2}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % 4taiaadgeacqGH9aqpcaWGHbWaaOaaaeaacaaIZaaaleqaaOGaeyO0 % H4Taam4uaiaad+eacqGH9aqpcaaIZaGaamyyaiabgkDiElaadAfacq % GH9aqpdaWcaaqaaiaaigdaaeaacaaIZaaaaiabec8aWjaac6cacaaI % ZaGaamyyamaaCaaaleqabaGaaGOmaaaakiaac6cacaaIZaGaamyyai % abg2da9iaaiodacqaHapaCcaWGHbWaaWbaaSqabeaacaaIZaaaaOGa % aiOlaaaa!5696! \Rightarrow OA = a\sqrt 3 \Rightarrow SO = 3a \Rightarrow V = \frac{1}{3}\pi .3{a^2}.3a = 3\pi {a^3}.\)
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
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