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
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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.
Thanks guys
Please tell me the answer and the workings
Cone:185 ml, Frustum:4815 ml
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Please how did you get 15. explain clearly please
(1/3)π(r^2/9)(h/3) = (1/81)πr^2h
Let the radius of the base be r and the height be h
(1/3)π r2 h = 5
πr^2 h = 15
The new cone will be similar to the original cone, the new height i h/3 and the new radius is r/3
volume of top cone
= (1/3)π(r^2/9)(h/3)
= (1/9)πr^2 h
= 15/9
= 5/3
the bottom fulcrum will be 15 - 5/3 = 40/3
check my arithmetic