a cone has a radiusof 12 inches anda surface area of 1050 square aches. Find the slant height of the cone to the nearest tenth of a inch

Now this one you will have to work backwards with me. First lets have a look at the formula for the surface area of a cone. This is Pi R^2 + Pi R L. Now we know the surface area so we can set up this equation. I will use 3.14in place of pi. 3.14 x 144 + 3.14 x 12 x L = 1050 in squared. Now we just solve for L. So 3.14 x 144 +3.14*12 = 489.84 Which means that L= 1050-489.84 = 560.16. L=560.16. (I rounded the 490.074). Now L is the length of the slanted edge like in this image.  So the height of the slant rounded to the nearest 10th of an inch is 560.2 in.

I hope this is correct and that it helped you.

-G

Go online to this calculator and enter your numbers in it. You will get a slant height of: = 15.8521 m

http://www.calculatorsoup.com/calculators/geometry-solids/cone.php

The surtace area is given by :

pi [r^2  + r L ]     where r is the radius and L is the slant height.....so we have

1050 = pi [12^2 + 12L]     divde both sides by pi

1050/pi  = 12^2  + 12L  

1050/pi = 144 + 12L    subtract 144 from both sides

1050/pi - 144   = 12L   divide both sides by 12

[ 1050/pi - 144] / 12  = L   = about  15.852  inches    [15.9 inches, rounded to the nearest tenth ]