1. A closed rectangular tank contains a certain amount of water. When the tank is placed on its \(\)3\(\) ft by \(\)4\(\) ft side, the height of the water in the tank is \(\)5\(\) ft. When the tank is placed on another side of dimensions \(\)4\(\) ft by \(\)5\(\) ft, what is the height, in feet, of the surface of the water above the ground?
(A) \(\)2\(\)
(B) \(\)3\(\)
(C) \(\)4\(\)
(D) \(\)5\(\)
(E) \(\)6\(\)
2. Water is poured into an empty cylindrical tank at a constant rate. In \(\)10\(\) minutes, the height of the water increased by \(\)7\(\) feet. The radius of the tank is \(\)10\(\) feet. What is the rate at which the water is poured?
(A) \(\)\frac{ 11 }{ 8\pi }\(\) cubic feet per minute.
(B) \(\)\frac{ 11 }{ 3\pi }\(\) cubic feet per minute.
(C) \(\)\frac{ 7 }{ 60\pi }\(\) cubic feet per minute.
(D) \(\)11\pi\(\) cubic feet per minute.
(E) \(\)70\pi\(\) cubic feet per minute.
3. The area of the base of a tank is \(\)100\(\) sq. ft. It takes \(\)20\(\) seconds to fill the tank with water poured at rate of \(\)25\(\) cubic feet per second. What is the height in feet of the rectangular tank?
(A) \(\)0.25\(\)
(B) \(\)0.5\(\)
(C) \(\)1\(\)
(D) \(\)5\(\)
(E) \(\)25\(\)
4. \(\)A, B\(\), and \(\)C\(\) are three unequal faces of a rectangular tank. The tank contains a certain amount of water. When the tank is based on the face \(\)A\(\), the height of the water is half the height of the tank. The dimensions of the side \(\)B\(\) are \(\)3 ft * 4 ft\(\) and the dimensions of side \(\)C\(\) are \(\)4 ft * 5 ft\(\). What is the measure of the height of the water in the tank in feet?
(A) \(\)2\(\)
(B) \(\)2.5\(\)
(C) \(\)3\(\)
(D) \(\)4\(\)
(E) \(\)5\(\)
5. What is the volume of a right circular cylinder with a radius of \(\)2\(\) and a height of \(\)4\(\)?
(A) \(\)8\(\)π
(B) \(\)12\(\)π
(C) \(\)16\(\)π
(D) \(\)32\(\)π
(E) \(\)72\(\)π
6. If a half-full \(\)4\(\)-inch by \(\)2\(\)-inch by \(\)8\(\)-inch box of soymilk is poured into a right circular cylindrical glass with radius \(\)2\(\) inches, how many inches high will the soymilk reach? (Assume that the capacity of the glass is greater than the volume of the soymilk.)
(A) \(\)8\(\)
(B) \(\)16\(\)
(C) \(\)\frac{ 4 }{ \pi }\(\)
(D) \(\)\frac{ 8 }{ \pi }\(\)
(E) \(\)\frac{ 16 }{ \pi }\(\)
7. If a right circular cylinder’s radius is halved and its height doubled, by what percent will the volume increase or decrease?
(A) \(\)50\(\)% decrease
(B) no change
(C) \(\)25\(\)% increase
(D) \(\)50\(\)% increase
(E) \(\)100\(\)% increase
8. A perfect cube has surface area \(\)96\(\). What is its volume?
9. A right circular cylinder has volume \(\)24\(\)π.
| Quantity A | Quantity B |
| The height of the cylinder | The radius of the cylinder |
10. How many \(\)2\(\) inch by \(\)2\(\) inch by \(\)2\(\) inch solid cubes can be cut from six solid cubes that are \(\)1\(\) foot on each side? (12 inches = 1 foot)
(A) \(\)8\(\)
(B) \(\)64\(\)
(C) \(\)216\(\)
(D) \(\)1,296\(\)
(E) \(\)1,728\(\)
Answers:
1 B
2 E
3 D
4 A
5 C
6 D
7 A
8 64
9 D
10 D
