Name Class Date copy A 1 Find two positive numbers whose product is 144 and whose sum is a minimum a 12 12 b 2 72 c 4 36 2 Consider the following problem A farmer with 760 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle What is the largest possible total area of the four pens 3 4 2 a 14540 ft b 14440 ft c 14460 ft d 14429 ft e 14463 ft f 14439 ft 2 2 2 2 2 If 2600 cm 2 of material is available to make a box with a square base and an open top find the largest possible volume of the box 3 a 12746 cm b 12857 cm c 12756 cm d 12777 cm e 12757 cm f 12780 cm 3 3 3 3 3 3 A rectangular storage container with an open top is to have a volume of 7 m The length of its base is twice the width Material for the base costs 15 per square meter Material for the sides costs 5 per square meter Find the cost of materials for the cheapest such container a 130 72 b 130 7 c 129 7 d 129 2 e 128 4 f 134 9 PAGE 1 Name Class Date copy A 5 Find the point on the line y 8x 6 that is closest to the origin a 48 7 64 64 b 47 6 65 65 c 50 7 65 65 d 48 6 64 65 e 48 8 65 65 f 48 6 65 65 6 Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L 3 cm if one side of the rectangle lies on the base of the triangle Round the result to the nearest tenth a 2 5 cm 1 8 cm b 1 5 cm 1 4 cm c 4 5 cm 0 3 cm d 1 cm 1 31 cm e 1 5 cm 1 3 cm f 6 5 cm 1 3 cm 7 A right circular cylinder is inscribed in a sphere of radius r 3 cm Find the largest possible surface area of such a cylinder Round the result to the nearest hundredth 2 a 96 5 cm b 90 39 cm c 91 5 cm d 91 52 cm e 92 cm f 91 4 cm 2 2 2 2 PAGE 2 2 Name Class Date copy A 8 A Norman window has the shape of a rectangle surmounted by a semicircle Thus the diameter of the semicircle is equal to the width of the rectangle If the perimeter of the window is 45 ft find the dimensions of the window so that the greatest possible amount of light is admitted Round the result to the nearest hundredth a base 12 58 ft height 7 3 ft b base 12 6 ft height 6 3 ft c base 13 6 ft height 6 27 ft d base 12 6 ft height 5 8 ft e base 12 71 ft height 6 3 ft f base 12 7 ft height 6 5 ft 9 A piece of wire 19 m long is cut into two pieces One piece is bent into a square and the other is bent into an equilateral triangle How should the wire be cut for the square so that the total area enclosed is a minimum Round the result to the nearest hundredth a 9 26 m b 7 16 m c 19 m d 8 31 m e 0m f 8 26 m 10 A fence 5 ft tall runs parallel to a tall building at a distance of 4 ft from the building What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building Round the result to the nearest hundredth a 12 90 ft b 11 60 ft c 12 69 ft d 13 70 ft e 14 73 ft f 12 70 ft PAGE 3 Name Class Date copy A 11 A conical drinking cup is made from a circular piece of paper of radius R 7 cm by cutting out a sector and joining the edges CA and CB Find the maximum capacity of such a cup Round the result to the nearest hundredth a 138 35 cm b 138 27 cm c 138 3 cm d 137 24 cm e 137 25 cm f 138 25 cm PAGE 4 3 3 3 3 3 3 Name Class Date copy A 12 A woman at a point A on the shore of a circular lake with radius 4 mi wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time She can walk at the rate of 7 mi h and row a boat at 3 mi h How should she proceed Find Round the result if necessary to the nearest hundredth a 0 65 radians b 0 49 radians c She should walk around the lake from point A to point C d She should row from point A to point C radians e 0 44 radians f 0 77 radians 13 Find an equation of the line through the point 6 12 that cuts off the least area from the first quadrant a y 3x 24 b y 2x 24 c y 2x 25 d y 2x 24 e y 3x 25 PAGE 5 Name Class Date copy A 14 Consider the figure below where a 8 b 1 and l 6 How far from the point A should the point P be chosen on the line segment AB so as to maximize the angle Round the result to the nearest hundredth a 3 83 b 4 14 c 3 17 d 4 43 e 3 13 f 3 3 15 A painting in an art gallery has height h 79 cm and is hung so that its lower edge is a distance d 12 cm above the eye of an observer as seen in the figure below How far from the wall should the observer stand to get the best view In other words where should the observer stand so as to maximize the angle subtended at his eye by the painting Round the result to the nearest hundredth a 31 69 cm b 35 57 cm c 36 4 cm d 33 05 cm e 31 93 cm f 33 14 cm PAGE 6 Name Class Date copy A 16 A steel pipe is being carried down a hallway 11 ft wide At the end of the hall there is a right angled turn into a narrower hallway 9 ft wide What is the length of the longest pipe that can be carried horizontally around the corner Round the result to the nearest hundredth a 27 04 ft b 28 27 ft c 27 21 ft d 28 94 ft e 28 24 ft f 28 29 ft 17 Find the maximum area of a …
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