Question

Find the surface area of this right cone.

5346π cm^2

1944π cm^2

1701π cm^2

1215π cm^2

Answer 1

l=(r^2+h^2)^1/2= 45
area= pi(r^2+rl)

Answer 2

The surface are of a cone have a standard formula \[A= \pi( r^2+rl)\]
where r is the radius of the base and l is length of lateral side. From figure of cinar you may get how he used pythgoras theorem to get the value for l. now just substitute it in the main formula

Answer 3

Yeah but can you go through all the steps? so i can try and figure this out .This is very difficult for me

Answer 4

o.k now pi*r*l is the lateral surface area (the area of curved surface ) and pi*r*r is the area of the base . we must add these to get total surface area.
In the figure we have r= 54/2 (radius of the base). and let h be the height of the cone and as i told l is length of lateral side....(the slanting part).
now if we look closer together l,r and h forms a right triangle
we know the values of h and r (h=36, r=27)
now from this calculate the value of l , piece of cake right , is just the hypotenuse of the right triangle using
\[l= {(r^2+h^2) }^{1/2}\]
we get l =(36*36+27*27)^1/2
l=(2025)^1/2
use calculator (*if required and find the root)
l= 45
now just use formula and find out the area of base and lateral surface. and add them together (remember pi*(r^2+rl) = pi*r^2+ pi*r*l)