34:I[547397,["/_next/static/chunks/1hcw-wnznq1q5.js","/_next/static/chunks/0et8ci25gg5au.js","/_next/static/chunks/3coghu6hk6rge.js","/_next/static/chunks/0f11_sazjytuj.js","/_next/static/chunks/2s0eicbrkx4ls.js","/_next/static/chunks/3jnfjb0iwbmv7.js","/_next/static/chunks/30y5yboqscjiy.js","/_next/static/chunks/2x4w4ke37diza.js","/_next/static/chunks/0zgfn2jvey-a0.js","/_next/static/chunks/3z1yzcb5ralmv.js","/_next/static/chunks/0fgl77uvipu1x.js","/_next/static/chunks/2_kp4n2-86oj-.js","/_next/static/chunks/1wng9dmtbytby.js","/_next/static/chunks/37al7_9w8mvn7.js","/_next/static/chunks/09ysjc67u1n4_.js","/_next/static/chunks/2u43ndstvg01b.js","/_next/static/chunks/2sohvx6xcul8d.js","/_next/static/chunks/04ef5hpllzq7a.js","/_next/static/chunks/3k2q8pjtt3ykz.js","/_next/static/chunks/1s-y8vjo1qwfr.js","/_next/static/chunks/2wge3pfyz4i-h.js","/_next/static/chunks/1v-zstwzw236u.js","/_next/static/chunks/0be3i--0b7dv0.js","/_next/static/chunks/3rn1zqcbchw96.js","/_next/static/chunks/2vlwhfwnhc8vs.js","/_next/static/chunks/17z03obgg_obf.js","/_next/static/chunks/0kecdk1_5bphe.js"],"default"] 36:I[839905,["/_next/static/chunks/1hcw-wnznq1q5.js","/_next/static/chunks/0et8ci25gg5au.js","/_next/static/chunks/3coghu6hk6rge.js","/_next/static/chunks/0f11_sazjytuj.js","/_next/static/chunks/2s0eicbrkx4ls.js","/_next/static/chunks/3jnfjb0iwbmv7.js","/_next/static/chunks/30y5yboqscjiy.js","/_next/static/chunks/2x4w4ke37diza.js","/_next/static/chunks/0zgfn2jvey-a0.js","/_next/static/chunks/3z1yzcb5ralmv.js","/_next/static/chunks/0fgl77uvipu1x.js","/_next/static/chunks/2_kp4n2-86oj-.js","/_next/static/chunks/1wng9dmtbytby.js","/_next/static/chunks/37al7_9w8mvn7.js","/_next/static/chunks/09ysjc67u1n4_.js","/_next/static/chunks/2u43ndstvg01b.js","/_next/static/chunks/2sohvx6xcul8d.js","/_next/static/chunks/04ef5hpllzq7a.js","/_next/static/chunks/3k2q8pjtt3ykz.js","/_next/static/chunks/1s-y8vjo1qwfr.js","/_next/static/chunks/2wge3pfyz4i-h.js","/_next/static/chunks/1v-zstwzw236u.js","/_next/static/chunks/0be3i--0b7dv0.js","/_next/static/chunks/3rn1zqcbchw96.js","/_next/static/chunks/2vlwhfwnhc8vs.js","/_next/static/chunks/17z03obgg_obf.js","/_next/static/chunks/0kecdk1_5bphe.js"],"TaskScreen"] 38:I[886109,["/_next/static/chunks/1hcw-wnznq1q5.js","/_next/static/chunks/0et8ci25gg5au.js","/_next/static/chunks/3coghu6hk6rge.js","/_next/static/chunks/0f11_sazjytuj.js","/_next/static/chunks/2s0eicbrkx4ls.js","/_next/static/chunks/3jnfjb0iwbmv7.js","/_next/static/chunks/30y5yboqscjiy.js","/_next/static/chunks/2x4w4ke37diza.js","/_next/static/chunks/0zgfn2jvey-a0.js","/_next/static/chunks/3z1yzcb5ralmv.js"],"IconMark"] 35:T638,[{"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Банк заданий","item":"https://fastege.com/bank"},{"@type":"ListItem","position":2,"name":"ЕГЭ по профильной математике","item":"https://fastege.com/bank/profilnaya-matematika"},{"@type":"ListItem","position":3,"name":"Задание 3","item":"https://fastege.com/bank/profilnaya-matematika?line=3"},{"@type":"ListItem","position":4,"name":"№525"}]},{"@context":"https://schema.org","@type":"LearningResource","@id":"https://fastege.com/bank/profilnaya-matematika/525","url":"https://fastege.com/bank/profilnaya-matematika/525","name":"Задание 3. Стереометрия, №525","description":"В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, диаметр которого в 5 раз меньше диаметра первого? Ответ выразите в сантиметрах.","learningResourceType":"Practice problem","educationalLevel":"ЕГЭ по профильной математике","inLanguage":"ru","isAccessibleForFree":true,"isPartOf":{"@type":"Collection","name":"ЕГЭ по профильной математике — банк заданий","url":"https://fastege.com/bank/profilnaya-matematika"},"provider":{"@id":"https://fastege.com/#organization"}}]23:["$","div",null,{"className":"mx-auto w-full max-w-6xl px-4 sm:px-6 flex flex-col gap-6 py-6 sm:py-10","children":[["$","nav",null,{"aria-label":"Хлебные крошки","className":"text-sm","children":[["$","$L1d",null,{"href":"/bank/profilnaya-matematika?line=3","className":"-ml-1 inline-flex items-center gap-1 rounded-md px-1 py-1.5 text-muted-foreground hover:text-foreground sm:hidden","children":[["$","$L34",null,{"ref":"$undefined","icon":{"name":"arrow-left","size":24,"node":[["path",{"d":"m12 19-7-7 7-7","key":"1l729n"}],["path",{"d":"M19 12H5","key":"x3x0zl"}]]},"className":"size-3.5","aria-hidden":"true"}],"Задание 3"]}],["$","ol",null,{"className":"hidden flex-wrap items-center gap-x-1.5 gap-y-1 text-muted-foreground sm:flex","children":[["$","$1","/bank",{"children":[false,["$","li",null,{"children":["$","$L1d",null,{"href":"/bank","className":"hover:text-foreground","children":"Банк заданий"}]}]]}],["$","$1","/bank/profilnaya-matematika",{"children":[["$","li",null,{"aria-hidden":"true","className":"text-muted-foreground/60","children":"/"}],["$","li",null,{"children":["$","$L1d",null,{"href":"/bank/profilnaya-matematika","className":"hover:text-foreground","children":"ЕГЭ по профильной математике"}]}]]}],["$","$1","/bank/profilnaya-matematika?line=3",{"children":[["$","li",null,{"aria-hidden":"true","className":"text-muted-foreground/60","children":"/"}],["$","li",null,{"children":["$","$L1d",null,{"href":"/bank/profilnaya-matematika?line=3","className":"hover:text-foreground","children":"Задание 3"}]}]]}],["$","$1","№525",{"children":[["$","li",null,{"aria-hidden":"true","className":"text-muted-foreground/60","children":"/"}],["$","li",null,{"children":["$","span",null,{"className":"font-medium text-foreground","aria-current":"page","children":"№525"}]}]]}]]}]]}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"$35"}}],["$","$L36",null,{"task":{"id":525,"name":"#3.93","shared_condition":null,"statement_html":"

В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, диаметр которого в 5 раз меньше диаметра первого? Ответ выразите в сантиметрах.

","answer_kind":"text","difficulty":0.28,"solve_rate":0,"attempts_total":0,"sources":[{"id":1,"title":"ФИПИ","kind":"ФИПИ"}],"lines":[{"id":3,"number":3}],"topics":[20],"progress":null,"has_solution":true,"similar_count":1,"exam":"profilnaya-matematika","exam_title":"ЕГЭ по профильной математике"},"similar":[{"id":526,"name":"#3.93 (ДЗ)","shared_condition":null,"statement_html":"

В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, диаметр которого в 6 раз меньше диаметра первого? Ответ выразите в сантиметрах.

Диаметр меньше в 5 раз — площадь основания меньше в $5^2=25$ раз. Из $\\pi r^2\\cdot2=\\dfrac{\\pi r^2}{25}\\cdot h'$: $h'=2\\cdot25=50$ см.

Ответ: 50.

"}}],"$L37"]}] 26:null 2a:[["$","title","0",{"children":"Задание 3. Стереометрия — №525, ЕГЭ по профильной математике"}],["$","meta","1",{"name":"description","content":"В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, ди…"}],["$","link","2",{"rel":"canonical","href":"https://fastege.com/bank/profilnaya-matematika/525"}],["$","meta","3",{"property":"og:title","content":"Задание 3. Стереометрия — №525, ЕГЭ по профильной математике"}],["$","meta","4",{"property":"og:description","content":"В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, ди…"}],["$","meta","5",{"property":"og:url","content":"https://fastege.com/bank/profilnaya-matematika/525"}],["$","meta","6",{"property":"og:site_name","content":"FastEGE"}],["$","meta","7",{"property":"og:locale","content":"ru_RU"}],["$","meta","8",{"property":"og:image","content":"https://fastege.com/og.png"}],["$","meta","9",{"property":"og:type","content":"article"}],["$","meta","10",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","11",{"name":"twitter:title","content":"Задание 3. Стереометрия — №525, ЕГЭ по профильной математике"}],["$","meta","12",{"name":"twitter:description","content":"В цилиндрическом сосуде уровень жидкости достигает 2 см. На какой высоте будет находиться уровень жидкости, если её перелить во второй цилиндрический сосуд, ди…"}],["$","meta","13",{"name":"twitter:image","content":"https://fastege.com/og.png"}],["$","link","14",{"rel":"icon","href":"/favicon.ico?favicon.1o5-z8nadw3ln.ico","sizes":"48x48","type":"image/x-icon"}],["$","link","15",{"rel":"icon","href":"/icon.svg?icon.42qp3n7_l984o.svg","sizes":"any","type":"image/svg+xml"}],["$","link","16",{"rel":"apple-touch-icon","href":"/apple-icon.png?apple-icon.29dj7vix-8pt8.png","sizes":"180x180","type":"image/png"}],["$","$L38","17",{}]]

Задание 3 №525 — ЕГЭ по профильной математике

Похожие задания