The height of a cone is 30cm. A small cone is cut off at the top by a plane parallel to the base.If its volume be of the volume of the given cone ,at what height above 1/27
the base is the section made?
Share
The height of a cone is 30cm. A small cone is cut off at the top by a plane parallel to the base.If its volume be of the volume of the given cone ,at what height above 1/27
the base is the section made?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
✿━━━━@♥Mg━━━━✿
______________________________
✿━━━━@♥Mg━━━━✿
Let the bigger cone be ABC and the smaller cone that is cut off the top be AFG.
Let the radius of the smaller cone be = r, and the height = h
and the radius of the bigger cone be = R, and the height = 30 cm (given)
Consider the triangle ADG and AEC
0 each)
so triangle ADG is similar to triangle AEC
=> AD/AE = DG/EC
=> h/30 = r/R ........................(1)
Also, Volume of the smaller cone = 1/27 (volume of bigger cone)
(1/3) pi r2 h = (1/27)(1/3) pi R2 (30)
h/30 = R2 /27r2 ..............(2)
from (1) and (2)
r/R = R2/27r2
27r3 = R3
=> R = 3r
Substituting the value of R in (1)
h/30 = r/3r
=> h = 30/3
=> h = 10
So, the height at which the section is made = 30 - 10 = 20 cm
________________________________♥
♥ʜᴀᴠᴇ ᴀ ɢᴏᴏᴅ ᴅᴀʏ..!♥
Step-by-step explanation:
hope it helps u......❣️