# If a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis, parallel to its base find the ratio of volume of two parts

2
by KPSINGH1

2016-03-19T17:59:23+05:30
Even I want the same answer
yeah you are right answer is right. its a ratio so the both volume will have 3 in denominator, and finally they will cancel each other. so answer is 2:7.
thanks
wlcm
2016-03-19T18:35:23+05:30
Let a cone of radius r = 10 cm
height = h cm

a/q,
volume of complete cone = πr²h/3
volume of part (i)  = π (r')² h/2
Volume of  part (ii) = total volume - Volume of  part(i)
= πr²h - π(r')² h/2
= πh{r² - (r')²/2}

Now,
l²  = r² + h²
⇒ r² = l² - h² -------------(1)

and
(l/2)² = (r')² + (h/2)²
(r')² = (l/2)² - (h/2)²

r' = r/2
⇒ (r')² =  r²/4
Now,
Volume of part (ii) = πh[r² - (r²/4)*(1/2)]
= πh(r² - r²/8)
= 7πhr²/8
And,
Volume of Part (i) = π(r/2)² h = πr²h/4
Ratio of volume of two parts = volume of part (i) ÷ volume of part (ii)
=  πr²h/4 ÷  7πr²h/8
= 2/7 =  2:7

answer is wrong i missed a denominator 3 of formula its pi r square h by 3.
bu t process is right
but on net the answer is 2:7
oops 1:7
hmmm solve it, then u will get the answer.