Question
Manoj has a set of blocks that are of the same height. The cone shaped block has a volume of 125 cubic inches. The sphere-shaped block has a volume of 250 cubic inches. What do you know about the radius of the base cone – shaped block?
Hint:
Since the blocks are of same height, the height of sphere-shaped block is the diameter of the block. So, the diameter of sphere block is equal to the height of cone block. Then we form two equations using the given information and solve the system of equations.
The correct answer is: The radius of the cone shaped block is (35156.25/π^2 )^(1/6).
Explanations:
Step 1 of 2:
Volume of cone shaped block = 
, r = base radius and h = height
Volume of sphere-shaped block = 
, h = diameter of the block
Given,
Step 2 of 2:
Also given, 
Final Answer:
The radius of the cone shaped block is 
.
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Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
