Cross Sections
Solids of Rotation
Volume
Cavalieri's Principle
Mixed Review
100
Name the cross section that would occur if you slice the cone vertically through the topmost point.
Triangle
100
The rectangle is rotated about the line shown. What 3D shape will be formed?
a. A cylinder with a radius of 5 and height of 3
b. A cylinder with a radius of 3 and a height of 5
c. A 6 x 5 x 3 rectangular prism
d. A cylinder with a radius of 6 and a height of 5
b. A cylinder with a radius of 3 and a height of 5
100
A cone and a cylinder both have the same height and radius. The cone's volume is
50pi " cm"^3
. What is the volume of the cylinder?
150pi " cm"^3
100
Do the figures have the same volume? Why or why not?
Yes; all cross sections have an equal area of 10 square units and both figures have a height of 6 units.
100
A machinist creates a solid steel part for a wind turbine. The part has a volume of 885 cubic centimeters. Steel can be purchased for $0.32 per kilogram and has a density of 7.95 g/cubic centimeter. If the machinist makes 450 of these parts, what is the total cost of the steel?
$1,013.15
200
Rectangle
200
What 3D shape will occur as a result of the rotation about the vertical line?
Sphere
200
How much larger is the first cylinder's volume than the second's?
4732pi
cubic units
200
According to Cavalieri's Principle, which pairs of shapes will have equal volumes?
a. A cylinder and sphere with the same diameter
b. A cylinder and cone with the same radius and height
c. A cone and triangular pyramid with equal base areas and heights
d. A cylinder and prism with equal base areas
c. A cone and triangular pyramid with equal base areas and heights
200
A right triangle is rotated 360 degrees about one of its legs. What 3D shape will occur from this rotation?
Cone
300
Which of the following could NOT be a cross section of the cone?
a. Triangle
b. Square
c. Oval
d. Circle
b. Square
300
What is the volume of the 3D shape that results from the rectangle being rotated about line m?
180pi "in"^3
300
A cone-shaped tank has a volume of
150pi " ft"^3
and a height of 2 feet.
What is the radius of the cone?
15 feet.
300
A pyramid has a height of 12 inches and a volume of 240 cubic inches. Which of the following figures could be the base of this pyramid? Select ALL that apply.
a. A hexagon with area 60 square inches
b. A right triangle with legs of 12 inches and 5 inches
c. A 12 inch by 5 inch rectangle
d. A 4inch by 5 inch rectangle
e. A triangle with base 10 inches and height 12 inches
A, C, E
300
A rectangle with a height of 7cm and width of 12cm is rotated continuously to form an object with a volume of
588pi " cm"^3
About which line could the rectangle have been rotated?
a. A long side
b. A short side
c. The vertical line of symmetry
d. The horizontal line of symmetry
a. A long side
400
Name all possible cross sections of a cylinder sliced parallel and perpendicular to its base.
Rectangle, Circle
400
A circle with a 5 inch radius is rotated about its vertical line of symmetry. What is the volume of the 3D figure that results from this rotation?
(500pi)/3 "in"^3
400
The prism shown has a cylindrical hole cut out of it. What is the volume of the figure? Round to the nearest whole number.
17,242 cubic centimeters
400
Two stacks of 23 quarters are shown. Do the two stacks of coins have the same volume? Why or why not? 
Yes; Both have the same cross-sectional area and the same height, so they have the same volume.
400
Find the volume of the figure. Use 3.14 for pi and round to the nearest foot.
463 cubic feet.