Subject
Quantitative Aptitude
Topic
Areas & Volumes
A vertical cone of volume V with vertex downwards is filled with water upto half of its height. The volume of the water is -
A vertical cone of volume V with vertex downwards is filled with water upto half of its height. The volume of the water is -
ক)
V/2খ)
V/4গ)
V/8ঘ)
V/16Explanation
( প্রশ্ন- V আয়তনের একটি লম্বআকৃতির শঙ্কুর শীর্ষবিন্দু নীচে অবস্থিত।এটিতে জলদ্বারা পূর্ণ করা হচ্ছে,যদি জলের উচ্চতা তার উচ্চতার অর্ধেক হয়,তবে জলের আয়তন কত?) ΔACE ও ΔBDC সদৃশকোণী ত্রিভুজে AC/BC =AE/BD AE=r,BD=r 1 AC=h, BC=h/2 =h 1 এখন, h/(h/2) =r/r 1 অতএব r/r 1 =2 বা, r 1 =(r/2) সম্পূর্ণ কোণকের আয়তন V=1/3πr 2 h ---- (1) পানিপূর্ণ অংশের আয়তন =1/3 πr 1 2h 1 =1/3π ×(r/2) 2 × h/2 =1/3π × r 2 /4 ×h/2 =1/8 (1/3πr 2 h) =V/8Related questions
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