So, I'm doing Surface Area of a Cone,
L= 7in
R= 8in
I calculated B (pi * 8^2) so B (also known as Area of Circle) = 200.96
Now I'm working on SA and a little confused,
SA=B+LA
=pi*8^2 + pi*8*7=11,429.6
but the next step in my equation says I should have 2 pi's (EXAMPLE; =pi (4)^2 + pi(4)(10) = 16pi + 40pi )
So could someone walk me through it? Thank you.
I'm assuming that L is the slant height, so your formula for total area is correct
pi R^2 + pi RL
I have no idea what the "next step" is supposed to be, since you already have the total area. Is 4 the radius of some other cone, with slant height 10?
If so, I suppose there must be some connection between the two cones ...
What have you left out?
I may not be understanding it, these are my sources for the formulas I'm using;
ht tps://sciencing.com/ calculate-base-cone-8178426.html (space in url)
ht tps://www.youtube.com/ watch?v=pkWED4nyCHA&list=PL_Z-HL5bvIMtchPQhzT731CS9U3010h2E&index=2&t=0s (space in url)
@1:00 He writes 2 sums with the pi symbol, is this specific to his problem ?
The 4 radius was the example he used, it isn't specific to my work, only Slant = 7 & Radius = 8. So 11,429.6 is already the surface area?
*phew.* All this math gets confusing & I try to over complicate it,.
Sure! I can help you understand the process.
To calculate the surface area of a cone, you need to calculate the area of the circular base and the lateral area. The formula for the surface area of a cone is SA = B + LA, where B is the area of the base and LA is the lateral area.
In your case, you have already correctly calculated the area of the base (B) using the formula B = π * r^2, where r is the radius of the base. For your cone, the radius (r) is 8 inches. So B = π * 8^2 = 200.96 square inches, which you have calculated correctly.
Now, let's move on to the lateral area (LA). The lateral area represents the curved surface of the cone. To calculate the lateral area, you need to find the slant height (l) of the cone. The slant height can be found using the Pythagorean theorem: l^2 = r^2 + h^2, where h is the height of the cone.
Unfortunately, you haven't provided the height of the cone, so we won't be able to calculate the specific slant height and lateral area for your cone.
However, I can explain how to proceed with the formula. Once you have the slant height, the lateral area (LA) can be calculated using the formula LA = π * r * l, where r is the radius of the base and l is the slant height. In your case, you would calculate LA as π * 8 * l.
Finally, you can calculate the total surface area (SA) by adding the area of the base (B) and the lateral area (LA) together: SA = B + LA. In your example, it would be SA = 200.96 + (π * 8 * l).
Remember to use the correct slant height (l) to ensure accurate results.