Question

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

Answer 1

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

Answer 2

(1/3)π(r^2/9)(h/3) = (1/81)πr^2h

Answer 3

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

Answer 4

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

Answer 5

Thanks guys

Answer 6

please how did you get 15

Answer 7

Good

Answer 8

How do you derive the formula

Answer 9

Thanks

Answer 10

Can you please explain clearly how you got the volume of the top cone?

Answer 11

U are good in mathematics wow
I wish I could do this

Answer 12

Please how did you get 15. explain clearly please

Answer 13

Thanks guys

Answer 14

Please tell me the answer and the workings

Answer 15

Cone:185 ml, Frustum:4815 ml

Answer 16

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.

Answer 17

Yes

Answer 18

Thank you, let me know if you have any more questions.

Answer 19

Ok

Answer 20

Great, feel free to ask me anything.

Answer 21

I have heard you

Answer 22

Alright, let me know if you need any assistance in the future. Have a great day!

Answer 23

Bye

Answer 24

Goodbye!