Similarity Ratio and Cross Section
What is the similarity ratio of perimeter?
a:b
General Prism
V=Bh or V=lwh
16. 12 math books are divided into two stacks as shown in the picture below. Assuming each book has the exact same dimension, use Cavalieri's principle to prove the volumes of the two stacks are equal.
Both have equal heights of 12, both have equal base of area of 1 textbook; Therefore volumes are equal.
Population Density Formula? Regular Density Formula?
Pop. Density= # of people/ area
Density= mass/ volume
11a and b. Sketch the cross sections of each solid.
a. cylinder (circle base) c. pyramid (triangle base)
What is the similarity ratio of area?
a2:b2
Cylinder
V=π r2h
8. 2 prisms with equal altitudes have equal volumes. The base of one prism is a square with side length of 5 inches. The base of the second prism is a rectangle with a side length of 10 inches, Determine and state in inches the measure of the width of the rectangle.
w=2.5 in
17. A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?
2.7 g/mL
12. The following right triangle is rotated about side AB. What is the resulting figure, and what is the volume of that shape?
Cone, v=753.98 mm3
What is the similarity ratio of volume?
a3:b3
What are the volume formulas made of? (lesson 4)
area of base x height
15. In a solid hemisphere, a cone is removed as shown. Calculate the volume of the resulting solid. In addition to your solution, provide an explanation of the strategy you used in your solution.
Calculate the volume of a hemisphere and a cone, then subtract to find the shaded area.
v=763.4
18. Gold has a density of 19.32 g/cm^3. If a square pyramid has a base edge length of 5cm and a height of 6 cm, and has a mass of 942 g, is the pyramid made of solid gold?
V=50 cm3, NOT solid gold :(
The following rectangle is rotates about line m. What is the resulting figure, and what is the volume of that shape.
Cylinder, v=1526.9 cm3