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