Solve problems on radicals

Question

Write the given , draw a figure then show the solution.

1. ) A cube has a surface area of 72 mm². Find the length of an edge of the cube.

2. A kite is secured to a rope that is tied to the ground . A breeze blows the kite so that the rope is taugh while the kite is directly above a flagpole that is 40ft from where the rope is staked down . Find the altitude of the kite if the rope is 100 ft long.

Answer 1

1

surface area = 72

surface area = 6 * e^2, where e is length of edge

so 6 * e^2 = 72

e^2 =12

e = sqrt (4 * 3) = 2 * sqrt(3)

2 use the pythagorean theorem

100^2 = 40^ + alt^2

alt = sqrt(8400)

= 10 * sqrt(84) = 20 * sqrt(21)