Perimeter, Area & Volume — Quiz 4

Questions in this quiz (8)

1. A cone (volume formula $$V = \frac{1}{3}\pi r^2 h$$) originally has a volume of 120 cubic units. If the cone’s height is reduced to one-third and its radius is tripled, what is the new volume of the cone?

   • 360
   • 120
   • 40
   • 240

2. Alex is packing small cubes into a storage container. Each small cube has dimensions of $$3\times 3\times 3$$ inches. The storage container has dimensions of $$4\times 3\times 3$$ feet. What is the maximum number of cubes that can fit in the container?

   • 2304
   • 152
   • 3456
   • 2500

3. Carlos is decorating his square-shaped classroom. He wants to cover all four walls (excluding the floor and ceiling) with square picture frames. If the room has a volume of 1000 cubic feet and each picture frame has dimensions of 2 feet by 2 feet, what is the maximum number of picture frames he can fit on the walls without overlap?

   • 200
   • 500
   • 400
   • 100

4. A rectangular storage box has a square base with an area of 100 square units. The total volume of the box is 800 cubic units. What is the total surface area of the box, including all faces?

   • $$320$$
   • $$200$$
   • $$800$$
   • $$520$$

5. Point P of rectangle PQRS is located at (2,8) and point R is located at (10,3). What is the area of rectangle PQRS?

   • $$10$$
   • $$20$$
   • $$8$$
   • $$40$$

6. If the radius of a cylinder is tripled and its height is reduced by half, how does the volume of the cylinder change?

   • Becomes twice as large.
   • Becomes 3 times larger.
   • Becomes 4.5 times larger.
   • Becomes 3 times smaller.

7. After a rainstorm, city workers collected an estimated $$15000$$ cubic meters of water from a drainage system. If this water were spread in an even layer over an empty rectangular parking lot with dimensions $$75$$ meters by $$100$$ meters, approximately how many meters deep would the layer of water be?

   • Between 1 and 2
   • Between 1 and 3
   • Between 3 and 4
   • More than 4

8. A large square consists of four identical rectangles and a smaller square in the center. The perimeter of each rectangle is 24 inches.What is the area, in square inches, of the large square?

   • $$576$$
   • $$144$$
   • $$400$$
   • $$225$$