Page 23 - AG Unit 2 Capacity, Cavalieri, and Constructions

AG 2-8: Density and Design Problems with Geometry Pre-scribed
Geometry

Name _________________________________ Class______ Date ______

1. Helium is a gas lighter than air that is used in balloons. The density of helium is approximately 0.18
kilograms per cubic meter. You get 16 helium balloons for your 16th birthday, each with a volume of
15 cubic meters. How many kilograms of helium do the balloons contain? *

2. 30 students return to the classroom after playing outside at recess. Over the course of the next
hour, each person produces 800 BTUs (British Thermal Units). The room is 20 feet by 20 feet by
12 feet. How many BTUs per cubic foot were produced?

3. At 20∘C, skim milk has a density 1.033 kilograms per liter, while light cream has a density of 1.012
kilograms per liter.
a. At 20∘C, what is the mass of one gallon of skim milk if 1 liter is approximately 0.264
gallons?

b. At 20∘C, a container holding 9 liters of liquid is 9.108 kilograms. Does the container hold
skim milk or light cream?

4. A cylinder and a sphere each have a 9” radius and have equal volumes. How many inches tall is the
cylinder?

5. A toy company is developing a super-hyper-bouncy ball. The original design has a radius of 2cm. If
the company develops are larger size bouncer by extending the radius to 4 cm, meaning they are
doubling the size of the radius, how much more volume does the larger ball have?

6. What is the density of CO gas if 0.196g occupies a volume of 100 ml?

7. A block of wood 3 cm on each side has a mass of 27g. What is the density of the block? Hint: don’t
forget to find the volume of the wood.

8. 5. Silver has a density of 10.5 grams/cm and gold has a density of 19.3 g/cm . Which would have
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the greater mass, 5cm of silver or 5cm of gold? Prove it.
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Smarter problems:
9. A solid gold cube with 2 cm edges is dropped into a cylinder of water. The water level in the cylinder
rises by 1cm. What is the diameter of the cylinder? (Hint: I expressed volume in terms of r to find
this.) Round to nearest hundredth. ____ What is the density of the gold if the cube weighs 154.4
grams? ____

Numbers 1-5 from https://www.ck12.org/book/CK-12-Geometry-Concepts-Honors/section/9.6/