Finding Volume
Volume will always be area of the _______ time ________. If a figure comes to an ________ we divide by 3 (or multiply by 1/3)
base, height, apex
When we dilate a figure with a scale factor of k, we would dilate the area by what
k2
When we dilate an object with a scale factor of k, we would dilate the volume by what
k3
Solids of rotation will always have a _______ base.
List 1 example that cannot be a solid of rotation and 1 that can.
Circular.
Can't: Pyramids, Prisms
Can: Cylinder, Cone
Formula for finding density
Density = Mass ÷ Volume
Volume of a rectangular pyramid with a base length of 5, a base width of 6, and a height of 9
90 cubic units
45 square units
Dilated volume of a cube the has an original volume of 16 and dilated by a scale factor of 3
432 cubic units
Parallel cross sections will always be the shape of the _______
Base
Draw the circle that can help us remember the formulas for mass, density, and volume
Circle with M in the top half, and V & D below
Two 3D solids that come to an apex
Cone and pyramid
90 square units
Dilated volume of a solid that has an original area of 20 and dilated by a scale factor of .5
2.5 cubic units
Perpendicular cross section of a square pyramid
Triangle
We have a cylinder bottle with a density of .93 grams per cubic cm. And a mass of 450 grams. What is the volume of the cylinder.
483.87 cubic centimeters
Radius of a cylinder that has a height of 6 and a volume 301.6
301.6 = ℼ42(6)
Radius = 4
Original area of a square that has an area of 13.5 after a dilation using scale factor 3
1.5
Original volume of a prism that has a volume of 1920 after a dilation of scale factor 4
30 units cubed
We can ______ a 2D figure to create a pyramid or cone by using a center that is above the image and a scale factor that is between 0 and 1
Dilation
Mass of a solid that has a density of 1.4 and a volume of 55 cubic units
77 grams
The formula for finding volume will always be the area of the ________ times the ________. If the figure comes to an _______ then you divide by 3 (or multiply by 1/3)
base, height, apex
A triangle has an original area of 9 and a dilated area of 144. What is the scale factor
144
A solid has an original volume of 65 and a dilated volume of 47,385. What is the scale factor used?
9
Cavelieri's Principle states that if two figures have equal ________ at corresponding parallel cross sections, then those figures have equal volume
Area
Volume of a solid that has a density of 1.76 and a mass of 120 grams (round to nearest 100th)
70.59