A roof in the shape of a half-cylinder covers the a local soccer field so kids can play soccer year-round. The building has a length of 80 feet and a width of 50 feet. Calculate the lateral
area of the roof. Use = 3.14.

6,280 ft³

Step-by-step explanation:

To find lateral surface area, use the formula L = 2rh, then plug in the values:

L = 2(3.14)(25)(80)

L = 12,560 ft³

Since its a half cylinder, we have to divide this by 2:

12,560/2 = 6,280

So, the lateral area of the roof is 6,280 ft³

300pi

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1