# Height of Cone

Algebra

### Height of Cone

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.
Guest

### Re: Height of Cone

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

mail_dinko

Posts: 2
Joined: Sat Jul 23, 2011 3:31 pm
Reputation: 0

### Re: Height of Cone

+ 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

### Re: Height of Cone

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.
Guest

### Re: Height of Cone

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

leesajohnson

Posts: 208
Joined: Thu Dec 31, 2015 7:11 am
Location: London
Reputation: -33

### Re: Height of Cone

How many wrongs have to come before it is right....????

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

### Re: Height of Cone

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

### Re: Height of Cone

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/
Guest