1. anonymous

2. anonymous

do you know the formula for finding out the surface area of a cone?

3. anonymous

if not, it is $\pi (radius)^{2} + (\pi *radius* hypotenuse)$ In the given figure, the radius is denoted by r and the height of the cone is denoted by y. so, by pythogarus's theorem, the hypotenuse, denoted by x is $\sqrt{r ^{2}+y ^{2}}$

4. anonymous

all you need to do now is substitute the values of the radius and hypotenuse in the formula and you will have your answer

5. anonymous

i think its c, but i want a second opinion

6. anonymous

how did you get c?

7. anonymous

i did it but i lost the paper

8. anonymous

so, 138.23m^2 is the surface area. substituting in the formula, we get, $138.23 = \pi*2^{2}+\pi*2*\sqrt{2^{2}+y ^{2}}$ solve for y. x will be $\sqrt{2^{2}+y ^{2}}$

9. anonymous

10. anonymous

$138.23=12.56+6.28\times \sqrt{2^{2}+ y ^{2}}$

11. anonymous

how would i solve for y

12. anonymous

138.23=12.56+6.26(sqrt(4+y^2)) therefore 138.23-12.56 = 6.28(sqrt(4+y^2)) therefore (138.23-12.56)/6.28 = sqrt(4+y^2) therefore 4+y^2 = ((138.23-12.56)/6.28)^2 therefore y^2 = (((138.23-12.56)/6.28)^2) - 4 therefore y = sqrt((((138.23-12.56)/6.28)^2) - 4)

13. anonymous

so it would be b

14. anonymous

no, try again.

15. anonymous

nvm i thought we were solving for x

16. anonymous

you need to know the value of y to solve for x.

17. anonymous

because x = sqrt(r^2+y^2)

18. anonymous

y = sqrt((((138.23-12.56)/6.28)^2) - 4).. doing this i got 11.03

19. anonymous

lets take this one step at a time: 138.23-12.56 = 125.67 125.67/6.28 = 20.011 20.011^2 = 400.44 400.44-4 = 396.44 y = sqrt(396.44)

20. anonymous

19.9.. so e

21. anonymous

right, substituting x = sqrt(19.9^2+2^2) = sqrt(400.44) = 20.011 approximately

22. anonymous

thank you

23. anonymous

you are welcome. It is really easy once you know the formula. it is all a matter of substituting the correct values.