Geometry of Gift Giving

December 17, 2018

Vanessa bought some round holiday dessert plates to give as a gift to her friend. However, the store only had 5 of the 8 plates she wanted. (All of the plates are the same.) The stack of five plates measured 1.5 inches tall, and when two plates were removed from the stack the remaining stack of three plates had a height of 1 inch. When Vanessa finally has all 8 of the plates she wants, how tall will the stack of 8 plates be, in inches? Express your answer as a decimal to the nearest hundredth.

 

What is the height of just one of these plates, in inches? Express your answer as a decimal to the nearest tenth.

 

The circumference of each of these plates measures 25 inches. What is the number of inches in the diameter of each plate? Express your answer as a decimal to the nearest hundredth.

 

Once Vanessa has all eight plates, she wants to put them into a box that she will then wrap and give as a present. The store has boxes (rectangular prisms) of all sizes. What is the volume, in cubic inches, of the smallest box Vanessa can buy that has integer dimensions and will hold this stack of eight plates?

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