A community for students.
Here's the question you clicked on:
 0 viewing
Preetha
 one year ago
How do you calculate the surface area of a cone?
Preetha
 one year ago
How do you calculate the surface area of a cone?

This Question is Open

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434127734377:dw unravelling the cone will give us the surface area, so we do the following

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434127987313:dw if we make a circle and take a ratio and find the areas, we will be left with the area of the figure drawn in this image with \[A = \pi r y\] so now to take the surface area of a cone, we will have \[\huge SA = \pi r y + \pi r ^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We can arrive at the same formula with a bit of calculus. dw:1434138596071:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Revolve the curve about the xaxis to generate a surface: dw:1434138690167:dw The surface area is given by the integral \[2\pi\int_0^h\frac{r}{h}x\,dx\] where \(\dfrac{r}{h}x\) is the radius of each circular crosssection taken at a particular \(0\le x\le h\), and so multiplying by \(2\pi\) and taking the integral along this interval gives the "lateral" surface area as the infinite sum of circumferences. \[A_{\text{lateral}}=\frac{2\pi r}{h}\int_0^h x\,dx=\frac{\pi r}{h}(h^20^2)=\pi rh\] Add the area of the "base", which is a circle with radius \(r\) to get the formula \[A_{\text{cone}}=\pi rh+\pi r^2\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ah yes, I was going to use calculus as well but not sure whether or not Preetha knows it, nice one Siths!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.