Q: If 20 solid gumballs with diameter 1 inch are placed inside a hollow sphere of diameter 6 inches, how much empty space is there in the larger sphere?
Answer:
Explanation:
Q: What is the maximum number of boxes with dimensions 4”x5”x8” that can be packed into one large box with dimensions 20”x20”x24”?
Answer: 60
Explanation: First, decide that a whole number of small boxes will entirely fill the large box. To do this, look at the dimensions and match them. 4″ fits into 20″ five times. 5″ fits into 20″ four times. 8″ fits into 24″ three times. That means, you’ll get five rows of small boxes, four boxes per row, and three layers deep. So, the quickest way to get the answer is to multiply 5x4x3 = 60.
BUT if you don’t notice that, just do (large volume)/(small volume).
Large volume = 20x20x24 = 9600
Small volume = 4x5x8 = 160
(large volume)/(small volume) = 9600/160 = 60
Q: Two rectangular prisms have the same volume. Prism 1 has dimensions 4 ft, 5 ft, and 7 ft. Prism 2 has dimensions 14 ft, 4 ft, and x ft. What is the value of x?
Answer: 2.5
Explanation: Volume of a rectangular prism = (L)(W)(H)
Volume 1 = (4)(5)(7) = 140
Volume 2 = (14)(4)(x) = 56x
Since the volumes are equal, 56x = 140. x = 2.5