# Surface area, spanning angle,

1. Jan 23, 2009

### Rola

Hello,

Can you help me in this question ,

In part a I must find the volume of cup(cylinder)
In part b I must find radius but how can I find Area

In part c ,d I don't know how can I solve it??

What is spanning angle and surface area??

Note : this question from previous exam but I think this question is strange because In my course I study about (Sequences,functions,infinite series,matrices,vectors,equation of circle.

An ice cream shop offers 2 types of serving :cones and cylindrical cups . The ice cream cup is H=8cm in height , and D=6 cm in diameter...

(a) How much water the ice cream cup hold??

(b)if the ice cream cone height ,h=18 cm ,then what must be the area,A,and radius ,r,of the cone base ,for it to have the same volume as the cup??

(c)Find the general formula for the spanning angle Ф,of the sector made by the cone when it is split open on a flat surface .

(d)Find Surface Area S,of the ice cream cone with dimensions as in part (b)

if thickness,t=sqrt3/(5 pi) cm of the cone is made of edible matter such as sugar ...etc ,What is the volume of the matter that makes cone

2. Jan 25, 2009

### Gib Z

Rola, in order for us to help you, you have to show us some work, what you have tried yourself to get these questions done!!

Do you know the formulae for the volume/surface area of cones and cylinders? That would be a good place to start.

The spanning angle they are referring to is - if you imagine the curved surface of the cone as a sheet of paper, roll out the paper onto a flat surface and it will look like a sector of a circle. The spanning angle is the angle inside that sector.

Surface area is the area of the object if we were to unroll every curved part onto a flat surface, and also place the flat parts of the object onto the surface as well, and add up all the areas.

3. Jan 26, 2009

### Rola

(a)The amount of water that the ice cream cup hold=the volume of ice cream cup(cylinder)

Volume=pi*r^2*h=pi*(3)^2*8=72pi cm^3

==========================================

volume of cone=1/3*pi*r^2*h

after solving

r=2*sqrt3 cm

Area of base cone=pi*r^2=2*pi*sqrt3 cm^2

========================================

(c)-

after splitting the cone

the resulting shape will be sector

but how can I find the angle??

Firstly , I think that the angle =arc length *radius but then I recognize that is not true

because this is cone not circle ..

and i still encounter difficulty in part d and e

can you guide me??

4. Jan 26, 2009

### Gib Z

Your answer to a) is incorrect, but b) isn't. You have r correctly, but subbed it into the formula for Area incorrectly.

For c), There is a simple formula for the curved surface area of a cone, its $$SA = \pi r l$$ where r is the radius of the base of the cone, and l is the slant height. To work out the slant height, you should draw a diagram and think about Pythagoras.