Geometry Answers

3. A trough having a trapezoidal cross section is full of water. If the trapezoid is 3ft wide at the top, 2ft wide at the bottom, and 2ft deep, find the total force owing to water pressure on one end of the trough.
4. Find the total force on the dam due to the fluid pressure:
A.Rectangle 200ft wide, 15ft high; water 10ft deep

1.An airplane at an altitude of 4400ft is flying horizontally away from an observer. At the instant when the angle of elevation is 45 degrees, the angle is decreasing at the rate of .05 rad/sec. How fast is the airplane flying at the instant?
2.A building 8ft high is 27/8ft from a building. Find the length of the shortest ladder which will clear the wall and rest with one end on the ground and the other end on the building. Also, find the angle which this ladder makes with the horizontal.
3.A man is walking along a sidewalk at the rate of 5ft/sec. A searchlight on the ground 30ft from the walk is kept trained on him. At what rate is the searchlight revolving when the man is 20ft away from the point on the sidewalk nearest the light?
4.A ladder 15ft long leans against a vertical wall. If the top slides down at 2ft/sec, how fast is the angle of elevation of the ladder decreasing, when the lower end is 12ft from the wall?

2.A right triangle has hypotenuse of length 13 and one leg of length 5. Find the dimensions of the rectangle of largest areas which has one side along the hypotenuse and the ends of the opposite side on the legs of this triangle.
3.A closed box with a square base is to have a volume of 2000 cu. Inches. The material for the top and bottom of the box is to cost Php3 per square inch, and the material, find the dimensions of the box.
1.Find the dimensions of the largest circle that can be inscribed in a square of 12 inches.
1.A manufacturer makes aluminum cups of a given volume ( 16 in3 ) in the form of right circular cylinders open at the top. Find the dimensions which use the least material.
2.Find the dimensions of the right circular cylinder of maximum volume which can be inscribed in a right circular cone of altitude 10 and radius 12.

A piece of wire of length 52 m is cut into two parts. Each part is then bent to form a square. It is found that the combined area of two squares is 109 m^2. Find the measures of the sides of the two squares.

Two posts, one 8 feet high and the other 12 feet high, stand 15 feet apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the top of the posts. Where the stake should be placed, to use the least amount of wire?

A manufacturer makes aluminum cups of a given volume (16 cubic inches) in the form of right circular cylinders open at the top. Find the dimensions which use the least material.

Find the dimensions of the largest circle that can be inscribed in a square of 12 inches.

A right triangle has hypotenuse of length 13 and one leg of length 5. Find the dimensions of the rectangle of largest area which has one side along the hypotenuse and the ends of the opposite side on the legs of this triangle?

A box with square base is to have an open top. The area of the material in the box is to be 100 in square. What should the dimensions be in order to make the volume as large as possible?

Exercise: An ant lives on the surface of a cube with edges of length 7cm. It is currently
located on an edge x cm from one of its ends. While traveling on the surface of the cube,
it has to reach the grain located on the opposite edge (also at a distance xcm from one
of its ends) as shown below.
(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of
this length are there?
(ii) Find an x for which there are four distinct shortest length routes to the grain.