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Sixth Grade: Shapes Word Problems
A 10 meter ladder is leaning
A 10 meter ladder is leaning aganist a building. The bottom of the ladder is 5 meters from the building. How many meters high is the top of the ...
A circle with radius 5
A circle with radius 5 has its center at (4,1). the line x-2y+4=0 intersects the circle. find the intersections
The volume of the soda can
The volume of the soda can is fixed at 400 cubic centimeters. Use the volume with each radius to find the possible heights of different sized soda cans. Once the height column is completed calculate the surface areas. The results for radius are already given. Round the height to the nearest tenth and the surface area to the nearest whole number. The given radius are: 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 ...
A large pizza has a diameter
A large pizza has a diameter 35cm. Two large pizzas cost $19.99. A medium pizza has a diameter 30 cm. Three medium pizzas cost $24.99...
The hypotenuse of a right triangle
The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less that the longer ...
If a ladder is leaning against a building
If a ladder is leaning against a building, and the distance from the bottom of the ladder to the building is 8 ft. less than the length of the ladder, how high up the side of the building is the top of the ladder if the distance is 1 ...
Two satellites are orbiting earth
Two satellites are orbiting earth. The path of one has the equation x2 +y2 = 2250000. The orbit of the other is 200 km farther fro the centre of earth. In one ...
The area of a triangle
The area of a triangle is 30in
2. The base of the triangle measures 2 in. more than twice the height of the ...
Jerry has a window in his room
Jerry has a window in his room. His window is a triangle. If angle one measures 63 degrees, and angle two measures 77 ...
The mainsail of a lightning sailboat
The mainsail of a lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24 ft tall mainsail has a leech length of 26ft and if Dacron sailcloth casts $10 per square ...
A sailboat has a triangular sail
A sailboat has a triangular sail with an area of 30 square feet. the height of the sail is 7 feet more than the length of the base of the ...
Sarah had an idea
Sarah had an idea, what would happen if you put a golf ball inside a basketball? How much room would there be inside the basketball afterwards. Her golf ball has a radius of 1.68 inches while her basketball has a diameter of 9.4 ...
Two ships leave port at same time
Two ships leave port at same time. Ship x is heading due north and ship y is heading due east. Twelve hours later they are 600 miles apart. If the ship x had traveled 480 miles from the ...
At noon, ship A is 150 km west of ship B
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h, How fast is the distance between the ships changing at 4:00 P.M.?
John is fencing his yard
John is fencing his yard that is 25 feet long and 40 feet wide. He wants to put fencing around the entire perimeter of his yard. The fencing he likes is $3 per ...
A semicircular window is to be laminated
A semicircular window of radius 12 inches is to be laminated with a sunblock coating that costs $0.75 per square inch to apply. What is the total cost of coating the ...
A clubhouse has a roof
A clubhouse has a roof whose slant height is 13 m and base is 24m. Two extra supports 2m and 3 m from the peak and perpendicular to the base of the peak need to be ...
Jim’s nephew owns a triangular plot of land
Jim’s nephew owns a triangular plot of land. The perimeter fence that surrounds the land measures 121 feet. The shortest side is 15 feet longer than one-half of the longest side. The second longest side is 4 feet shorter than the longest ...
When you buy a TV
When you buy a TV, the size refers to the diagonal. You have a cabinet that is 40 inches by 50 inches. You want to buy a 72 inch Plasma High Definition TV to watch the Super ...
The first Ferris wheel was built
The first Ferris wheel was built in 1893 in Chicago. Its diameter was 250 feet. What was the actual circumference of the Ferris wheel? Use 3...
Two triangles are similar
Two triangles are similar. One triangle is 4,2,3 the second one is 12,9,6.
Which fraction represents the ratio of the lengths of the sides of the small triangle to the lengths of the large triangle?
Is it 1/3 , 4/9, 1/2...
A road up a hill makes an angle
A road up a hill makes an angle of 5.1 with the horizontal. If the road from the bottom of the hill to the top of the hill is 2.5 miles ...
A trapezoid has a slant height
A trapezoid has a slant height of six meters. The trapezoid has an interior height of 9 meters. on one base it measures 5 meters and on the last one measures 77 ...
The legs of a right triangle
The legs of a right triangle are 5 and 7 centimeters long, respectively. What is the length of the hypotenuse? If ...
Every time the pedals go through
Every time the pedals go through a 360 degree rotation on a bicycle, the tires rotate 3 times. If the tires are 24 inches in ...
Tom and Carol are playing a shadow game
Tom and Carol are playing a shadow game. Tom is 6 feet tall and carol is 5 feet tall. If Carol stands at the shadow top of Tom's head, there is two combined shadows total 15 ...
The measure of the largest angle
The measure of the largest angle of a triangle is 12 degress less than the measures of the other two. The smallest angle measures 58 degress less than the largest ...
A street that is long is covered in snow
A street that is long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn times in traveling the length of the street. What is the diameter of the tire?
Use π = 3.14. Round your answer to the nearest ...
In a certain triangle, the second side
In a certain triangle, the second side is one-third of the first side in length. The third side ia 2 meters less than the first side. The perimeter of the triangle is 26 meters. Form an algebraic equation to express the problem, and identify the variables,...
From a space probe orbiting Jupiter’s moon Io
From a space probe orbiting Jupiter’s moon Io from an altitude of 552 km, it was observed that the angle of depression from the probe to the surface of this moon was 39.7 degrees. What is the radius of the ...
The answer for the second angle
The answer for the second angle in a triangle is three times as large as the frist. the third angle is one third as large as the second angle. Find the angle ...
Trapezoids
The trapezoid has a slant length of 6 inches. The interior length is 10 inches. The bases are 5 ...
Given a trapezoid where the small base
Given a trapezoid where the small base is 6 greater than the height and the larger base is 4 greater then three times the height, find all three dimensions (small base, large ...
A square animal pen
A square animal pen and a pen shaped like an equilateral triangle have equal ...
trapezoids
What is the perimeter of a trapezoid if the base is 10 and height is 15?
perimeter
An olypmpic swimming pool is twice as long as its width. The perimeter of the pool is 150 ...
A triangle has a perimeter
A triangle has a perimeter of 197 centimeters. The sum of the smallest and medium sides is 49 cm more than the longest side. The difference of the longest side and shortest sides is 22 ...
There is a total of 1800 sq ft office space
There is a total of 1800 sq ft office space. The amount of space allocated per person is increased by 25 ft when 6 people are removed. How many people share this renovated space after the ...
Deshawn wants to build a fence
Deshawn wants to build a fence around a rectangular space in his backyard. The space is 5 yards long and 3 yards wide. The fence section are 1 yard ...
A square courtyard has a side
A square courtyard has a side length of 50 yards. The city plans to add x yards to each side so that it can pour a sidewalk around ...
The lenght of a rectangle
The lenght of a rectangle is 30cm less then three times the width. the perimeter of this rectangle is 180...
A triangle has a perimeter
A triangle has a perimeter of 161 miles. Each of the 2 smaller sides of the triangle is two-thirds the length of the longest ...
The outside walls of a house
The outside walls of a house are 2 meters high and the amount you can spend for outside wall materials cannot go over $7500. For each material at the cost given, what is the greatest perimeter the house could have? Wood at $53 per square meter, Stucco at $57 per square meter, Brick at $65 per square ...
