Honors Geometry

Name__________________

Displacement and Density:

Block_____________

1. A stone is placed in a graduate cylinder whose diameter is 5 cm, causing the water level in the cylinder to rise 2.7 cm. What is the volume of the stone?

2. A 141 gram steel marble is submerged in a rectangular prism with base 5 cm by 6 cm. The water rises 0.6 cm. What is the density of the steel?

3. A toy submarine with a mass of 325 grams raises the water level of a 50 x 40 cm aquarium 0.3 cm. What is the density of the submarine?

4. The density of an NBA basketball is 0.05 oz/in3. If the circumference of the basketball is 29.5 inches, find the mass.

5. While Sid hikes in the Gold Country of northern California, he dreams about the adventurers that walked the same trails years ago. He suddenly kicks a small bright yellowish nugget. Could it be gold? Sid quickly makes a balance scale using his walking stick and finds that the nugget has the same mass as his 165 gram nutrition bar. He then drops the stone into his cylindrical water bottle, which has a 2.5 cm radius, and notes that the water level goes up by 0.9 cm. Has Sid struck gold? Explain your reasoning. (The density of gold is 8.97 g/cm3)        

Fruit Boxes  A grocer wants to sell strawberries in small boxes. He wants to make the boxes from a square card 30  cm long and 30 cm wide as shown below.                             The shaded areas are cut away and the rest is folded along the dashed lines. The sides are folded up and  stuck together using flaps. The lid has two flaps that are not glued.  A.  Calculate the volume of the box.      B. What if the 7 cm changes to x?  What would be the volume of the box?      C.  Suppose the grocer starts with the same square of card, but changes the 7 cm to different  measurements. What is the largest volume he can make the box?  Show all work and justify your  solution using PEA.  

Displacement, Density & Fruit Boxes WS_2015.pdf

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