Volume
Volume+ (Trig and Combined Shapes)
Surface Area
Density
Working Backwards (Volume and Density)
Nets, Cross Sections, and Axes of Rotation
100
What is the difference between a prism and pyramid?
Prism- same shape all the way through/ flat top and bottom
Pyramid- Shape gets smaller as it comes to 1 singular point
100
What do we do to find volume if we have 2 shapes put together?
Find 2 volumes separately, then add them together
100
What is surface area?
The total area of the surface of a shape.
Or, the area of all its faces added together.
100
What is the formula for density?
density = (mass)/(volume)
d = (m)/(v)
100
What are the steps when working backwards to find a specific measure?
EX. find height given radius and volume
Step 1: Choose your formula
Step 2: Plug in what you know
Step 3: Solve for what you need
100
What 3D figure would these nets form (if any)?
Cube
200
What is the volume of the cylinder?
pi*8^2*7=1407.43
200
Find the volume to the nearest tenth.
Note: The top "hemisphere" is half of a sphere
2881.9 ft3
200
Which figure has the largest surface area?
Figure A
200
A box with a volume of 200 cm3 holds 432 g of sodium chloride. What is the density?
2.16 g/cm3
200
If a box has Density = 1.8 g/ml and Volume = 39.7 ml, what is its mass?
Mass = 71.5 g
200
What is the horizontal cross section of a cone?
Circle
300
What is the volume of the triangular prism?
1/2(3*4)*3=18
300
Find the volume to the nearest tenth.
Note: The bottom "hemisphere" is half of a sphere
315,371.9 cubic feet
300
What is the surface area of this cube?
486 cm^2
300
A block of iron has the dimensions of 2 cm x 3 cm x 2 cm. If the mass is 94 grams, what is the density?
7.83 g/cm3
300
If an object has Density= 3.6 g/ml and Mass= 17.8 g, what is its volume?
Volume=4.9 ml
300
What 3D figure would this net form (if any)?
Pyramid
400
What is the volume of the sphere?
4/3*pi*8^3=2144.66
400
v_(text(cylinder))=pi3^2*18=162pi
v_(text(sphere))=4/3pi3^3=36pi
v_(text(remaining))=v_(text(cylinder))-3v_(text(sphere))
v_(text(remaining))=162pi-3(36pi)= 52pi
400
Find the surface area:
684 square inches
400
The Kowloon Walled City was an ungoverned area of Hong Kong, home to numerous criminal groups and the most densely populated place in the world until it was cleared and demolished by authorities in 1993. In 1987, it had a population of 33,000 living in 0.026 sq kilometres of land. What was the population density of the Kowloon Walled City in 1987?
33000/0.0026 = 1,269,231 people/square kilometre.
400
Find the height of a cone with a diameter of 8 feet and a volume of 100.48 cubic feet.
100.48= 1/3 pi 4^2h
h=6 ft
The height of the cone is 6 feet.
400
The following center-pivot irrigation system is roughly the shape of a rectangle, with height 20 feet and length 200 feet. It rotates around a tower at one of its ends to water a field. Which 3D shape approximately represents the space that the irrigation system passes through?
Cylinder
500
Find the volume of a rectangular pyramid with length 5 feet, width 6 feet, and height 7 feet.
70 cubic feet.
500
What is the volume of the cylinder?
h=8
r=8*sqrt(3)=13.8564
V=1/3pi*13.8564^2*8=1608.49
500
What is the surface area of the sphere?
SA=4pir^2=4pi8^2=256pi " or "804.248
500
A cylinder has a radius of 5 cm and a height of 2 cm. It has a mass of 250 grams. What is the density?
And if the density of water is 1- will it sink or float?
v= pir^2h= pi*5^2*2 = 157.1 cm^3
d= m/v 250/157.1 = 1.5915 g/cm^3
Density is 1.5915. Since 1.5915>1 it is denser than water, so will sink.
500
Find the height of the triangular pyramid if the base of the triangle is 5 feet, the height of the triangle is 10 feet, and the volume of the pyramid is 20 cubic feet.
The height of the pyramid is 2.4 feet.
500
What 3D figure will be formed by the rotation of circle m around axis y?
Torus (donut)