Height of Cone

[Guest]

An ice cream cone has the following description:

Diameter of cone: 2 in.

Top of ice cream: shape of hemisphere.

Cone is to hold 8 cu. in. of ice cream.

Determine height of cone.

Let h = height.


Volume of cone: 1/3 x pi x r^2 x h

Volume of sphere: 4/3 x pi x r^3

Unsure how to proceed.

[mail_dinko]

The volume [tex]V=8[/tex] cubic in includes 1/2 sphere (out of the cone, top)+ one whole cone volume. Lets say these are [tex]V_1[/tex] and [tex]V_2[/tex] respectively.
[tex]V=V_1+V_2[/tex]
[tex]V= \frac {1}{2}.\frac {4}{3} \pi r ^3 + \frac {1}{2} \pi r ^2 h[/tex]
Since [tex]d=2 \rightarrow \fbox {r=1}[/tex]
[tex]8= \frac {1}{2}.\frac {4}{3} \pi + \frac {1}{2} \pi h |.6[/tex]
[tex]48= 4 \pi + 3 \pi h \rightarrow \fbox {h = \frac {48-4 \pi}{3 \pi}}[/tex]
[tex]h=3,76 in[/tex]

[Guest]

+ 1/2πr 2 h : I don't understand the 1/2 added.

h = 48 - 4pi / 3pi : I don't understand subtracting the 4pi.


Thanks.

[Guest]

typo error in earlier post I think 1/2 instead of 1/3 for cone bit
V=V1+V2
V=1/2 x 4/3 x Pi x r^3 + 1/3 x Pi x r^2 x h

Since d=2, r=1

8=1/2 x 4/3 x Pi + 1/3 x Pi x h
8 = 2.09 + 1.05 x h
h = 3.7 ins

[Guest]

Thanks again.

[leesajohnson]

V=V1+V2
V=1/2 x 4/3 x Pi x r^3 + 1/3 x Pi x r^2 x h
here r= 1 and d= 2

h = 3.7

[Guest]

How many wrongs have to come before it is right....????
What about this for an answer.....?????

Volume is 8 cu ins, equals half sphere + cone .... Radius = 1

So 4/6 * Pi * r^3 + 1/3 * Pi * r^2 * h = 8

then 4/6 * Pi + 1/3 * Pi * h = 8 .... because r = 1

multiply across by 3 gives

..... 2 * Pi + Pi * h = 24

...... Pi * h = (24 - 2 * Pi)

...... h = (24 - 2 * Pi) / Pi

...... Height h = 5.639 ins.

[Guest]

It may be neater to do the simplifying as below.......

multiply across by 3 gives

..... 2 * Pi + Pi * h = 24

..... Pi * (2 + h) = 24

..... 2 + h = 24 / Pi

..... h = (24 / Pi) - 2

..... Height h = 5.639 ins.

[Guest]

VOLUME OF A CONE IS EQUAL TO THE ONE-THIRD PART OF THE CYLINDER THAT IS=

VOLUME OF CYLINDER = πR*RH
SO, VOLUME OF A CONE IS = 1/3πR*RH http://volumeofcone.online/