Scaling
Cross sections
Volume
Missing Measurements
Story Problems
100
How would you solve the following equation?
x3 = 8
100
What is the definition for Cavalieri’s principle?
If two solids are cut into cross sections by parallel planes, and the corresponding cross sections on each plane always have equal areas, then the two solids have the same volume.
100
What is the formula for finding the volume of a pyramid?
Volume = Area of base x height divide 3
100
I made a tower in the shape of a rectangular prism out of blocks. The length was 8 in, width was 2 in, and height was 4 in. What was the volume of the figure?
64 in3
200
A polygon with area 10 square units is dilated by a scale factor k.
Find the area of the image of each value of k=1.5
22.5 square units
200
Slide 2
No, the area of the base is the same, but since they have different heights, their volumes are different.
200
Slide 4
484 km^3
200
What is the length of the missing side? The volume of this rectangular prism is 600 units3.
5 units
200
Prince Bobby is filling his pool with hot fudge. His pool is 6 feet deep, 12 feet long, and 5 feet wide. How many cubic feet of fudge will Prince Bobby need to fill his pool.
6 x 12 x 5=360 ft3
300
A solid with volume 12 cubic units is dilated by a scale factor of k.
Find the volume of the image for each given value of k=0.4.
0.768 cubic units.
300
Slide 3
Yes they do. For both
Area of base = 6
Height = 5
300
Slide 5
10 in^3
300
Find the height.
~~7
300
A pyramid has a square base with a side length of 8 centimeters. The height of the pyramid is 6.
What is the volume?
128 cm3
400
Johnny is creating a flyer for the school play. The flyer originally has an area of 120 square inches. The flyer Johnny prints will be a dilation of the flyer using a scale factor of 3.
What will be the area of the of the flyer be?
1080 square inches
400
What volume of silver metal will weigh exactly 1255 g?
The density of silver is 5 g/cm^3
251 cm^3
400
The density of oil is 750 kilograms per m^3. An object floats in oil if its density is less than oil's density, and it sinks if its density is greater than oil's. Suppose a block of steel has a mass of 1500 kilograms which is in the shape of a rectangular prism. The dimensions of the prism are 2 by 3 by 4.
Will the block of steel sink or float in oil? Explain or show your reasoning.
The block of steel will float since it's density is 125 kg per m^3 while the density of oil is 750 kg per m^3.
500
A cube with side length 4 centimeters has a density of 2 grams per cubic centimeter. What is its mass?
128 grams