## wafflegod551 3 years ago An image of an ice cream cone is shown below. The slant height of the cone itself is 3.5 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? 4.3π square inches 3.8π square inches 5.4π square inches 3.2π square inches

1. wafflegod551

2. SmoothMath

"An image of an icecream cone is shown below" False promises. >:(

3. wafflegod551

look at attachments lol

4. SmoothMath

Notice that the scoop is just half of a sphere. So you can use the formula for the surface area of a sphere, but then divide by 2.

5. SmoothMath

6. wafflegod551

lol you didn't o.o

7. wafflegod551

makes me want an icecream cone now -.-

8. SmoothMath

The formula for the surface area of a cone is Pi*r*s, where r is the radius and s is the slant height. Now, this doesn't include the surface area of the circle BETWEEN the cone and the scoop, but we don't want it to. So we're good. Add those two surface areas.

9. SmoothMath

Let's go get icecream then! =D

10. wafflegod551

cant im stuck doing geometry :(

11. wafflegod551

ooo yay meh first fan thx :D

12. mubzz

In order to solve this, you need to know the equations to calculate the surface areas of a cone and a sphere. We will do this in two parts. 1) Surface area of the cone - the cone is made of a circular base so you can find the radius from this section. - the diagonal of the cone is referred to as the slant height and is often referred with 'l' Surface area of cone = pi*r*l = pi*3.5*0.75 = 2.625pi 2) Surface area of half sphere - formula for calculating surface area of sphere is 4pi*(radius)^2 - since you have a semi-sphere, your formula will become \[2pi*r ^{2}\] = 1.125pi 3) Add the answers from one 1 and 2 Surface area = 3.75pi squared inches, which when rounded up will be 3.8pi squared inches. Hope that helps :)

13. wafflegod551

thank you all