Solid Rotations
Cross Sections
Scaling & Area
Volume & Scaling Solids
Applications and Formulas
100
This 3D shape is formed when a rectangle is rotated around one of its longer sides. (along the axis of rotation)
What is a cylinder?
100
This shape is the cross section of a sphere cut horizontally.
What is a circle?
100
If a shape is scaled by a factor of 3, this is how much larger its area is.
What is 9 times larger?
100
What happens to a solid’s volume when scaled by a factor of 2?
Hint: If K=2, what is the factor for VOLUME?
What is the volume increases by 8 (2³)
K=3; K3=27
100
A telescope increases the area shown by a scale factor of 5, How much larger is the image viewed through the telescope then with the naked eye?
What is 25 times larger.
New Area = Area * k2.
200
This solid is formed when you rotate a right triangle around one of its legs.
What is a (right) cone?
200
A vertical slice through the center of a cylinder creates this shape.
What is a rectangle?
200
This kind of graph can represent the relationship between scale factors and area.
Hint: If the factor for area is K2, what operation do we apply to find K? --- "We take the _____ ____!"
What is a square root graph?
200
This is the formula for the volume of any prism or cylinder.
2x DOUBLE JEOPARDY 2x
What is V = Bh?
400 POINTS!!!
200
Two fish tanks are in a Pet Store The larger tank can hold 800 cm³ of water. If the difference between the large and small tank is a scale factor of 2. How much water can the smaller fish tank hold?
The small tank can hold 100 cm3 of water.
300
This solid is formed when a semicircle is rotated around its diameter.
2X DOUBLE JEOPARDY 2X
What is a sphere?
600 POINTS!!!
300
This is the shape you get if you cut a cone horizontally.
A circle (that is smaller than the base).
300
A triangle has an area of 10 in². If it’s scaled by 0.5, this is the new area.
What is 2.5 in²?
300
The cross-section of a prism cut horizontally has an an area of 24 in2. If the prism has a height of 10 in. What is the volume of the prism.
What is 240 in3?
300
This is the formula for the volume of any pyramid.
What is V = ⅓Bh?
400
The picture shows a man using a telescope. This 2D shape produced the multiple cylinders forming the telescope.
What is a rectangle?
400
This shape results from slicing a cyclinder diagonally.
What is an oval?
400
A square with side length 4ft is dilated by a factor of √2. This is the area of the new square.
2x DOUBLE JEOPARDY 2X
What is 32 ft2?
800 POINTS!!!
400
This is the volume of a cone with radius 3 and height 6 (do not multiply by pi).
What is 18π?
400
If a cube's side length is tripled (side length * 3), by this factor does its volume increase.
Hint: If K=3, what is the factor for VOLUME?
What is 27 or (3³)?
27 = 3*3*3
K=3; K3=27
500
A construction worker uses a drill bit shaped like a triangle. When the bit spins, it carves out a hole in the shape of a 3D solid. This is the shape of the hole created.
Hint: What does the original triangle represent?
What is a cone?
The triangle represents the cross-section.
500
This 3D solid has all circular cross sections, regardless of the slicing plane’s angle.
What is a sphere?
500
Explain how scale factors affect the area of a pyramid’s cross sections.
Cross sections are scaled versions of the base, and the area is multiplied by the square of the scale factor (k²).
500
A solid is scaled by k. How much would the surface area and volume change.
What is the surface area scales by k², volume by k³?
500
A solid metal object has a mass of 500 grams. The object is put into a weightless boat that has an original volume of 100 cm³. If the volume is increased by a scale factor of 2. Find the new density of the boat (Density = mass/volume). Will it float or sink in the water? .
Hint: Water's Density = 1g/cm3. Anything with a density larger than this will sink.
New Volume = 800cm3.
The new density is 500/800 = 0.625 g/cm3. The boat will float.