Surface area of a cone Q please answer... I need to finish my summer hw fast?

Question

how do i get the surface area of a cone

I don't know how to get the slant height

the dimensions are: true height: 9 base radius 7
thank u very much

Answer 1

Hello...to figure out the slant value, look at the triangle made by the base radius of 7 and the height of 9. Your slant value is c.

a^2+b^2=c^2

7^2+9^2=c^2

Then use the formula for surface area of a cone!

Answer 2

Consider the cone to be a triangle in x-y rotated around the y axis. So y goes from 0 to 9 and x at y=0 is 7.

The triangle is formed by x axis, y axis and a line that goes from (7,0 to (0,9)

m = (9 - 0)/(0 - 7) = -9/7 and y intercept is 9 so:
y = -9x/7 + 9

area of surface = A

If s is along the surface of the cone then:
dA = 2pi x ds

s = SQRT(x^2 + y^2)
s = SQRT(x^2 + (81/49)x^2)
s = xSQRT(1 + 81/49) = xSQRT(130/49)
s = (x/7)SQRT(130) and ds = SQRT(130)/7

dA = 2pi [SQRT(130)/7] xdx
A = (pi/7)SQRT(130)x^2 from 0 to 7
A = 7piSQRT(130)

The above is if this is for calc. If not then the formula for the surface area of a cone is:

piR SQRT(H^2 + R^2)

R = radius of base
H = height