The document contains 8 math word problems involving geometry, algebra, and physics concepts. Problem 1 asks to find the minimum value of the sum of two numbers' cubes given their sum. Problem 2 asks for the shape of a rectangle with minimum fencing given a fixed area and one unfenced side. Problem 3 asks for the dimensions of a rectangular field divided into 3 lots to minimize fencing.

1. Removal Exam
1. The sum of two numbers is k. Find the minimum value of the sum of their cubes.
2. A rectangular field of a given area is to be fenced off along the bank of a river. If no fence is needed along the river. What is the
shape of the rectangle requiring the least amount of fencing?
3. A rectangular field of fixed area is to be enclosed and divided into three lots parallel to one of the sides. What should be the relative
dimensions of the field to make the amount of fencing a minimum?
4. A box to be made of piece of cardboard 9 in. square by cutting equal squares out of the corners and turning up the sides. Find the
volume of the largest box that can be made in this way.
5. Water flows into a vertical cylindrical tank at 12 cu. ft per min, the surface rises 6 in per min. Find the radius of the tank.
6. A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft per sec, find how fast the lower end is
moving when it is 16 ft from the wall.
7. A triangular trough 10 ft long is 4ft across the top and 4ft deep. If the water flows in at the rate of 3 cu. ft. Find how fast the surface
rising when the water is 6 in. deep.
8. A boy on a bike ride north 5 mi., then turn east. If he rides 10 mph, at what rate was his distance to the starting point S changing
2hrs after he left that point?
Removal Exam
1. The sum of two numbers is k. Find the minimum value of the sum of their cubes.
2. A rectangular field of a given area is to be fenced off along the bank of a river. If no fence is needed along the river. What is the
shape of the rectangle requiring the least amount of fencing?
3. A rectangular field of fixed area is to be enclosed and divided into three lots parallel to one of the sides. What should be the relative
dimensions of the field to make the amount of fencing a minimum?
4. A box to be made of piece of cardboard 9 in. square by cutting equal squares out of the corners and turning up the sides. Find the
volume of the largest box that can be made in this way.
5. Water flows into a vertical cylindrical tank at 12 cu. ft per min, the surface rises 6 in per min. Find the radius of the tank.
6. A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft per sec, find how fast the lower end is
moving when it is 16 ft from the wall.
7. A triangular trough 10 ft long is 4ft across the top and 4ft deep. If the water flows in at the rate of 3 cu. ft. Find how fast the surface
rising when the water is 6 in. deep.
8. A boy on a bike ride north 5 mi., then turn east. If he rides 10 mph, at what rate was his distance to the starting point S changing
2hrs after he left that point?
Removal Exam
1. The sum of two numbers is k. Find the minimum value of the sum of their cubes.
2. A rectangular field of a given area is to be fenced off along the bank of a river. If no fence is needed along the river. What is the
shape of the rectangle requiring the least amount of fencing?
3. A rectangular field of fixed area is to be enclosed and divided into three lots parallel to one of the sides. What should be the relative
dimensions of the field to make the amount of fencing a minimum?
4. A box to be made of piece of cardboard 9 in. square by cutting equal squares out of the corners and turning up the sides. Find the
volume of the largest box that can be made in this way.
5. Water flows into a vertical cylindrical tank at 12 cu. ft per min, the surface rises 6 in per min. Find the radius of the tank.
6. A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft per sec, find how fast the lower end is
moving when it is 16 ft from the wall.
7. A triangular trough 10 ft long is 4ft across the top and 4ft deep. If the water flows in at the rate of 3 cu. ft. Find how fast the surface
rising when the water is 6 in. deep.
8. A boy on a bike ride north 5 mi., then turn east. If he rides 10 mph, at what rate was his distance to the starting point S changing
2hrs after he left that point?
Removal Exam
1. The sum of two numbers is k. Find the minimum value of the sum of their cubes.
2. A rectangular field of a given area is to be fenced off along the bank of a river. If no fence is needed along the river. What is the
shape of the rectangle requiring the least amount of fencing?
3. A rectangular field of fixed area is to be enclosed and divided into three lots parallel to one of the sides. What should be the relative
dimensions of the field to make the amount of fencing a minimum?
4. A box to be made of piece of cardboard 9 in. square by cutting equal squares out of the corners and turning up the sides. Find the
volume of the largest box that can be made in this way.
5. Water flows into a vertical cylindrical tank at 12 cu. ft per min, the surface rises 6 in per min. Find the radius of the tank.
6. A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft per sec, find how fast the lower end is
moving when it is 16 ft from the wall.
7. A triangular trough 10 ft long is 4ft across the top and 4ft deep. If the water flows in at the rate of 3 cu. ft. Find how fast the surface
rising when the water is 6 in. deep.
8. A boy on a bike ride north 5 mi., then turn east. If he rides 10 mph, at what rate was his distance to the starting point S changing
2hrs after he left that point?