Question

An image of an ice cream cone is shown below.



The slant height of the cone itself is 4 inches, and the radius of the ice cream scoop on top is 0.75 inches. What is the approximate surface area of the entire ice cream cone with the scoop of ice cream?

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0805_09/image0024e848b52.gif

Answer 1

Am I doing this right?? \[\pi(0.75)(4)+\pi(0.75)^{2}\]

Answer 2

Well Done..

Yes you are right.

Answer 3

Now this is where I'm stuck.. how do i solve this in terms of pi?

Answer 4

\[Surface \; Area (Cone) = \pi r l + \pi r^2\]

Answer 5

You can use:

\[\pi = 3.14\]

Answer 6

If this is right here is where I'm stuck

\[\pi(3)+\pi(0.5625)\]

Answer 7

Now factor out \(\pi\)..

Answer 8

\[\pi(3)+\pi(0.5625) \implies \pi(3 + 0.5625)\]

Add the brackets first..

Answer 9

Okay so my answer would round up to be
\[(3.6)\pi\]

Answer 10

Is that the whole cone plus the scoop of ice cream on top?

Answer 11

If you want to leave it in \(\pi\) then yes your answer is right..

Answer 12

No I think..

Answer 13

Above is semi sphere..

You have to include surface area for that too I think..

Answer 14

Yeah. So use surface area of a hemisphere to find that and add them together?

Answer 15

\[Surface \; Area(Sphere) = 4 \pi r^2\]

So its half will be:

\[SA = 2 \pi r^2\]

Answer 16

Do I still use 0.75 as my radius?

Answer 17

Yes..

Answer 18

4.7π

Answer 19

Total ??

Answer 20

Yes..

Answer 21

for surface area of cone, you don't need the pi*r^2 because it has the scoop of ice cream so the bottom of cone is not included

Answer 22

I agree..

Answer 23

So I get \[(1.125) \pi \] and I add that to \[(3.6)\pi \] and my answer is 4.725 or \[(4.7)\pi\]

Answer 24

They want the surface area of the cone and the scoop of ice cream on top.

Answer 25

Just subtract \(0.5625 \pi\) from the final answer..

Answer 26

Because in this case Surface Area will be:

\[SA = \pi rl + 2 \pi r^2\]

Answer 27

\[SA = 3 \pi + 1.125 \pi \implies SA = 4.125 \pi\]