the volumeof a right circular cone is 5 litres. calculate the volumes of the two parts into which the cone is divided by a plane parallel to the base one third of the way down from the vertex to the base to the nearest ml
volume of the right circular cone=1/3pi*r2*h=5
pi*r2*h=15
from the third part of the statement,the radius(r)=1/3r.the height(h)=1/3h
the volume of the cone=1/3*pi*(1/3r)2*1/3h
=1/3pi*1/9r2*1/3h
=1/3*1/9*1/3*pi*r2*h
From equation one above pi*r2*h=15
=1/81*15=~0.185
~185mL
volume of the frustum=5 - 0.185=~4.815=~4815mL
Volume of the right circular cone= 1/3pi *r^2×h = 5
pi x r^2 ×h = 15
: r=1/3, h= 1/3
The volume of the cone = 1/3 × pi ×(1/3r) 2×1/3h
= 1/3 pi x1/9r^2x1/3h
From eqn 1
Pi x r^2 x h = 15
1/81× 15 = 0.185 or 185ml.
Volume of frustum = 5 - 0.185= 4.815ml
Thanks guys
Good
Thanks
Can you please explain clearly how you got the volume of the top cone?
U are good in mathematics wow
I wish I could do this
please how did you get 15
How do you derive the formula
The solution is:
Volume of right circular cone = 1/3 * pi * r^2 * h = 5 L
Therefore, pi * r^2 * h = 15 (multiplying both sides by 3)
Now, the plane bisects the cone into 2 similar cones. Let the height of the smaller cone be h1 and its radius be r1.
So, h1/h = r1/r = 1/3 (given)
Now, the volume of the top cone can be found as:
V1 = 1/3 * pi * r1^2 * h1 = 1/3 * pi * (r/3)^2 * (h/3) = (1/81) * pi * r^2 * h
V1 = (1/81) * 15 * pi = 0.185 L or 185 mL (approx)
The volume of the frustum can then be found as:
Vfrustum = Vcone - V1
Vfrustum = 5 - 0.185 = 4.815 L or 4815 mL (approx)
Therefore, the volumes of the top cone and the frustum are 185 mL and 4815 mL (approx) respectively.