1. ## Spanning angle,surface area,.....

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. Originally Posted by Diligent_Learner
Hello,

Can you help me in this question ,

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??

this is the formula for a cylinder
$V=[pi](r^2)h$

Height $8cm$

D= $6 cm$ convert to radius that will be 3cm

$V=[pi](r^2)h$

$V= 3.142(3)^2(8)$

$V=226.22cm^3$

so the volume of the cylindrical cup is $V=226.22cm^3$

3. (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??
The volume of a cone is $\frac13 \pi r^2h$

In part b I must find radius but how can I find Area
The base of the cone is circular so one you have the radius you can use the formula for the area of a circle, $A = \pi r^2h$

(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 .
The length of the arc formed by the split open cone will be the same as the circumference of the base ie. $2\pi r$. The radius of the spread out cone will be $\sqrt{r^2+h^2}$. What will the spanning angle be?

(d)Find Surface Area S,of the ice cream cone with dimensions as in part (b)
Use the split open cone. The area of a full circle that size would be $\pi (\sqrt{r^2+h^2})^2$ and the fraction of that circle you have in the cone is $\frac{\phi}{2\pi}$. Don't forget to add the area of the base as well.

4. thank you princess_21 and badgerigar for helping me ..

but I have a question :
badgerigar :How the arc length =circumference of circle
arc is portion of circle ?

5. badgerigar :How the arc length =circumference of circle
arc is portion of circle ?
There are 2 circles involved, the base of the cone and the large circle that the arc is a part of. The arc length is equal to the circumference of the base of the cone. If this is not immediately obvious, watching this wolfram demonstration might help.