CLEAR
Toprankers-Info

+91 7676564400

Mobile App

Get it on Google Play
Discussions
Select Date
Tags:

Articles

Discussions
Submit Discussion
MA Afroz

· started a discussion

· 1 Months ago

volume of frustum (Question: 107672.0 )

Vol of frustum=total vol - vol of smaller cone.
Above way is simple rather than the one which provided.

Question:

If a cone is cut into two parts by a horizontal plane passing through the mid point of its axis, the ratio of the volumes of the upper part and the frustum is:

Options:
A) 1 : 1 
B) 1 : 2  
C) 1 : 3 
D) 1 : 7
Solution:




Knowledge Expert

· commented

· 1 Months ago

Dear Student,

Yes you are right. we can solved it another way.

its volume V = (1/3)(π)(R²)(H) cu. units = (πR²H)/3

2) As the horizontal plane cuts the cone into two parts through the mid point of its axis, the height of the cone is divided into two equal parts, forming a top cone of height H/2 units. If the base radius of the top cone is r units, then r/(H/2) = R/H [Since the vertical angle of both are same].

Solving, r = R/2 units.

Hence volume of the small cone at the top = v = (1/3)(π){(R/2)²{(H/2) cu. units
Simplifying, v = (πR²H)/24 cu. units

So volume of the bottom part (frustum) = V - v = (πR²H)/3 - (πR²H)/24 = 7(πR²H)/24 cu. units

3) So ratio of their volumes, Top part : Bottom part = (πR²H)/24 : 7(πR²H)/24 = 1:7

Keep learning with us!
Best wishes
Team Toprankers
-logo
We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.
More About
-Info
-Info

Mobile App

Get it on Google Play
About Us Campus Ambassador Careers Contact Us Refund Policy

All Rights Reserved Top Rankers

User Policy
Disclaimer
Terms & Conditions