Answer :


Let ‘H’ be the height of cone ‘R’ be the radius of base of cone.


R = 10 cm


When the cone is cut at midpoint of H by a plane parallel to its base we get a cone of height H/2 and a frustum also of height H/2


Let the radius of the base of the cone which we got after cutting and the radius of upper circle of frustum be ‘r’ as shown in figure


From figure consider ΔABC and ΔADE


ABC = ADE = 90˚


BAC = DAE …(common angle)


as two angles are equal by AA criteria we can say that


ΔABCΔADE



r = 5 cm


Let Vc be volume of the cone and Vf be the volume of frustum


Volume of cone = (1/3)π(radius)2(height) cm3


Vc = (1/3) × π × r2 × (H/2) cm3


= (1/3) × π × 52 × (H/2) cm3


= (1/3) × π × 25 × (H/2) cm3


Volume of frustum = (1/3)πh(R2 + r2 + Rr) cm3


Vf = (1/3) × π × (H/2)(102 + 52 + 10 × 5) cm3


= (1/3) × π × (H/2) × 175 cm3



The ratio of volumes of two parts after cutting = Vc:Vf = 1:7


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigo Marathon Part 2Trigo Marathon Part 2Trigo Marathon Part 245 mins
Trigo Marathon Part 1Trigo Marathon Part 1Trigo Marathon Part 146 mins
Application of Trigo Important QuestionsApplication of Trigo Important QuestionsApplication of Trigo Important Questions44 mins
Arithmetic Progression and 'nth' Term of APArithmetic Progression and 'nth' Term of APArithmetic Progression and 'nth' Term of AP55 mins
Chemical Properties of Metal and Non MetalChemical Properties of Metal and Non MetalChemical Properties of Metal and Non Metal61 mins
Extraction of MetalExtraction of MetalExtraction of Metal56 mins
Purification of MetalsPurification of MetalsPurification of Metals60 mins
Properties of Metal and Non MetalProperties of Metal and Non MetalProperties of Metal and Non Metal59 mins
Introduction of Metal and Non MetalIntroduction of Metal and Non MetalIntroduction of Metal and Non Metal59 mins
Heights and Distances - IIHeights and Distances - IIHeights and Distances - II45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses