A right circular cylinder with a radius of 2 feet and a length of 6 feet is cut into three equal pieces. What is the volume, in cubic feet, of each of the three pieces?
Question 1
A right circular cylinder with a radius of 2 feet and a length of 6 feet is cut into three equal pieces. What is the volume, in cubic feet, of each of the three pieces?
2π
3π
8π
12π
24π
Question 2
| Quantity A | Quantity B |
|
Three times the total surface area of a cube with edge length of 1 centimeter |
The total surface area of a cube with edge length of 3 centimeters |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 3
E is the center of square ABCD.
AB = 8
| Quantity A | Quantity B |
| AE | 4 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 4
Each edge of the cube shown above has length n. What is the perimeter of quadrilateral ABDE?
4n
2n2
Question 5
ABCG and CDEF are squares with the same area touching at point C. ∠BCD is a right angle.
| Quantity A | Quantity B |
|
3 times the length of AB |
The length of AE |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 6
The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?
729 – 162
729 – 81π
729 – 9π
729
Question 7
What is the total surface area of a cube with a volume of 512?
384
320
256
152
48
Question 8
The total surface area of a cube is 54.
| Quantity A | Quantity B |
|
The length of a diagonal of one face of the cube |
3 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 9
Cube C has an edge of 4 and cube D has an edge of 5.
| Quantity A | Quantity B |
|
The ratio of cube C’s total surface area to its volume |
The ratio of cube D’s total surface area to its volume |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 10
A certain building is a rectangular solid with a square base of side length 25 meters and a volume of 13,000 cubic meters. What is the volume, in cubic meters, of a building that has a square base with a side of 75 meters and the same height as the other building?
1,444.4
4,333.3
39,000
117,000
351,000
Question 11
Marty has a right circular cylindrical pool of diameter 12 feet and his neighbor, Rusty, has a right circular cylindrical pool of diameter 18 feet. If the depths of the pools are equal, then the volume of water in Rusty’s pool is how many times that in Marty’s pool?
1.5
2.25
2.5
4
4.25
Question 12
A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of ∠BAC is four times that of ∠ACB, and the height of the cylinder is equal to the diameter of its base, then the volume of the shaded region is what fraction of the volume of the entire cylinder?
Question 13
Jack is storing a rectangular box inside a cylindrical container. The container has a volume of 980π cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?
Indicate all such values.
3 inches by 6 inches by 12 inches
6 inches by 9 inches by 15 inches
10 inches by 10 inches by 10 inches
8 inches by 9 inches by 16 inches
11 inches by 15 inches by 18 inches
9 inches by 9 inches by 20 inches