Please help Expert and Above Only! I will double the points if you can explain it! Both questions please!

Problem 11

Work Shown:

The surface area of a 3D sphere is 4pi*r^2. So a hemisphere has surface area 2pi*r^2 since we cut the surface area in half.

Plug in r = 6 (half of the diameter 12) and we get 2pi*r^2 = 2pi*6^2 = 72pi

Now consider the circle with radius r = 6. Its area is pi*r^2 = pi*6^2 = 36pi

Add the two areas and we get 72pi+36pi = 108pi

Lastly, use your calculator to get 108pi = 108*3.1415926535898 = 339.292006587699 which rounds to 339

Problem 12

Explanation:

Look at where the "0" in the bottom sliding portion lines up with the number scale above. That "0" is between 19 and 20 mm. So you could argue that 19.2 and 19.5 are both valid answers, but I think 19.5 is the better answer since the tickmark seems to be right in the middle (more or less).

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: