May Problem of the Day2013

Problem Solving

May 1, 2013

A magnifying glass is a lens that makes objects appear larger than they really are. Suppose a 35°angle is observed through a magnifying glass that enlarges objects to twice their actual size. How big is the angle when viewed through this magnifying glass? Explain your answer.

May 2, 2013

The Pythagorean Theorem states a² + b² = c², where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. Find the length of the hypotenuse if the legs of a right triangle measure:

1) 3 in. and 4 in. 2) 9 in. and 12 in.

May 3, 2013

The Pythagorean Theorem states a² + b² = c², where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. The length of a leg and the length of a hypotenuse are listed below (the hypotenuse is the longest segment). Find the length of the other leg. If needed, express your answer as a square root (radical form).

1) 6, 72) 1, 53) 5, 10

May 6, 2013

The most practical and efficient kitchen is designed as a “work triangle.” The ideal distances of the sides of the triangle are: 4 to 6 ft, 4 to 7 ft, & 4 to 9 ft. What is the largest perimeter of the ideal work triangle? What is the smallest perimeter of the ideal work triangle

May 7, 2013

A checkerboard contains 8 squares along the sides of the board and 8 squares along the top and bottom. Each of these squares is 1 by 1. The total number of 1 by 1 squares is 64. Find the total number of squares on a checkerboard (include 2 by 2 squares, 3 by 3 squares, and so on).

May 8, 2013

Square area is A = s². Each side of a checkerboard measures 40 cm. The board contains 8 rows of 8 squares per row. Find the area of each small square on the board.

May 9, 2013

Rectangular area is A = lw. The size of the dollar bill of today is smaller than the dollar bills printed before 1929. The dimensions of those bills were 7.2 by 3.13 inches. The bills in circulation today are 6.14 by 2.61 inches. Find the area of each and determine about what percentage has our dollar bill reduced its’ area?

May 10, 2013

Rectangular area is A = lw. In 1897 the recommended size for a chicken house was given as “ten feet is wide enough and every ten feet in length will afford space for 15 hens.” According to this advice, find the area of a coop that could accommodate 60 hens.

May 13, 2013

Rectangular area is A = lw. Roofing shingles are packaged in groups called “squares”. One square covers 100 square feet of a roof. The roof of a house is made of two rectangles, each 13 feet by 36 feet. The two rectangles meet to form the peak of the home. How many squares of shingles are needed?

May 14, 2013

Rectangular area is A = lw. A 1-inch by 12-inch rectangle has an area of 12 square inches. A standard sheet of letter size paper is 8½ inches by 11 inches and has an area of 93.5 square inches. Pete claims he can cut a 1-inch by 12-inch rectangle from this paper. Explain how he can do this and what is the area of the remaining paper?

May 15, 2013

Formula for the area of a circle is A = πr². A beam of light from a lighthouse may be seen for 30 miles in all directions. What is the area in square miles in which the light may be seen? What factors might interfere with the light being seen in this area?

May 16, 2013

Formula for the area of a circle is A = πr². A CD that is 120 mm in diameter can hold up to 74 minutes of music. The unrecorded portion of this disc has a diameter of 50 mm. Find the area of the recorded portion of this disc.

May 17, 2013

Formula for the area of a circle is A = πr². The diameter of an archery target is 48 inches. The diameter of the innermost circle is 9.6 inches. What percentage of the area of the target is the area of the smallest circle?

May 20, 2013

Two pizzas have a 12-inch diameter. One pie is cut into eight equal slices, and the other is cut into 6 equal slices. If the 8 slice pie sells for $1 a slice, what would be the cost per slice of the 6 slice pie so that you would make at least the same amount of money per pie?

May 21, 2013

Volume of a rectangular prism is V=lwh. A shoe box measures 6.5 inches by 3.5 inches by 12 inches. How many boxes of this size can be place on a 12-inch shelf if the shelf is one foot from the ceiling? What is the volume of wasted space?

May 22, 2013

The surface area of a 3-Dimensional figure is the sum of the areas of all the faces and bases of the figure. Dice are cubes with 6 faces. Each side of a die is a face. Twelve ¾ by ¾ by ¾ inch dice are boxed in two layers of two rows of three dice per row (six dice are in each layer). Find the surface area of the box.

May 23, 2013

The Smith family likes to take trips in the car. Traveling south on the highway, the Smiths will pass cutoffs for three cities: Allenville, Browning, and Cooperton. The distance from Allenville to Browning is 16 miles. The distance from Browning to Cooperton is 8 miles, and the distance from Allenville to Cooperton is 24 miles. What town is between the other two?

May 24, 2013

Slopes are used in planning and constructing roofs of buildings. The slope of a roof is called the pitch. You can find the pitch of a roof with the following formula. Pitch = rise of the roof ÷ ½ the span of the roof. If the rise of the roof is 0 feet and the span is 24 feet, find the pitch. Compare the pitch of a roof to the slope of a line, using the formula slope = rise/run.

May 28, 2013

Rachael the roofer is carrying shingles over her shoulder and a bucket of nails as she is climbing up the ladder to the roof. The total weight she is carrying is 75 lbs. the shingles weigh 4 times as much as the nails. How much do the nails and the shingles weigh?

May 29, 2013

Paul the painter had to paint three walls each of different heights. The tallest wall, which will be painted white, is 12’ taller than the wall that is to be painted blue. The difference between the white wall and the red wall is 8’ more than the difference between the red wall and the blue wall. If the blue wall is 8’ feet in height, how tall are the other two walls?

May 30, 2013

Sharon was told by her boss to hoist up a load of cinderblock to the second story of the building under construction. She asked her boss how much the load of cinderblock weighed. The boss replied that it weighed 400 pound plus ⅓ of the total weight. Scratching her head, Sharon tried to figure out what the boss just said. Can you figure out the weight of the cinderblocks?

May 31, 2013

At a construction site two masons were building brick wall. Each wall of bricks requires 10 pounds of mortar. While building the wall a little of the mortar is left over. After four walls are built there is enough mortar to build another wall. If the masons start the day with 160 pounds of mortar, how many walls can be built?