i had to do the answer as a pic cuz my iPad is gonna die.
sorry <:)
The effective rate is calculated in the following way:
![r = {(1 + \frac{i}{n} )}^{n} - 1](https://tex.z-dn.net/?f=r%20%3D%20%20%7B%281%20%2B%20%20%5Cfrac%7Bi%7D%7Bn%7D%20%29%7D%5E%7Bn%7D%20-%201)
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers:
Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder
Area of the base of the cylinder =
![\pi r^{2} = 8^{2} \pi =64 \pi](https://tex.z-dn.net/?f=%20%5Cpi%20r%5E%7B2%7D%20%3D%208%5E%7B2%7D%20%5Cpi%20%3D64%20%5Cpi%20)
Area of the cylinder 'wall' = width × length =
![12](https://tex.z-dn.net/?f=12)
×
![2r \pi](https://tex.z-dn.net/?f=2r%20%5Cpi%20)
=
![12](https://tex.z-dn.net/?f=12)
×
![16 \pi](https://tex.z-dn.net/?f=16%20%5Cpi%20)
=
![192 \pi](https://tex.z-dn.net/?f=192%20%5Cpi%20)
Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by
![\pirl](https://tex.z-dn.net/?f=%20%5Cpirl)
where
![l](https://tex.z-dn.net/?f=l)
is the slanted height of the cone
SA of cone =
![\pi (8)(10)=80 \pi](https://tex.z-dn.net/?f=%20%5Cpi%20%288%29%2810%29%3D80%20%5Cpi%20)
Hence total painted surface area is
Slope: 3/2
Y-Intercept: -3