Card 1 of 20
EasyStudy card 1
Prompt
What defines a right cylinder?
Answer
Two congruent parallel circular bases joined by a perpendicular altitude.
MathChapter 20: Surface Areas and Volumes
Flashcards
Cylinders and Spheres Flashcards
Twenty concise cards on cylinder and sphere structure, formulas, great circles, composites, holes, scaling, nets, and conversions.
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Card 2 of 20
EasyStudy card 2
Prompt
What is cylinder volume?
Answer
\(V=\pi r^2h\).
Card 3 of 20
EasyStudy card 3
Prompt
What is cylinder lateral area?
Answer
\(LA=2\pi rh\).
Card 4 of 20
EasyStudy card 4
Prompt
What is total area of a closed cylinder?
Answer
\(TA=2\pi rh+2\pi r^2\).
Card 5 of 20
EasyStudy card 5
Prompt
What is sphere surface area?
Answer
\(SA=4\pi r^2\).
Card 6 of 20
EasyStudy card 6
Prompt
What is sphere volume?
Answer
\(V=\tfrac43\pi r^3\).
Card 7 of 20
EasyStudy card 7
Prompt
What is a great circle?
Answer
A sphere section whose plane passes through the center.
Card 8 of 20
MediumStudy card 8
Prompt
How does a cylinder's curved surface unwrap?
Answer
Into a rectangle of height h and width 2πr.
Card 9 of 20
MediumStudy card 9
Prompt
How do you recover radius from circumference C?
Answer
\(r=C/(2\pi)\).
Card 10 of 20
MediumStudy card 10
Prompt
What is hemisphere volume?
Answer
\(\tfrac23\pi r^3\), half the volume of a sphere.
Card 11 of 20
MediumStudy card 11
Prompt
In a sphere inscribed in a cylinder, what is cylinder height?
Answer
The sphere diameter, 2r.
Card 12 of 20
MediumStudy card 12
Prompt
What is the sphere-to-cylinder volume ratio in that exact inscribed configuration?
Answer
2/3.
Card 13 of 20
MediumStudy card 13
Prompt
How is a coaxial cylindrical hole handled?
Answer
\(V=\pi h(R^2-r^2)\).
Card 14 of 20
MediumStudy card 14
Prompt
If cylinder radius scales by a and height by b, how does volume scale?
Answer
By \(a^2b\).
Card 15 of 20
MediumStudy card 15
Prompt
Why is 1 ft³ equal to 1728 in³?
Answer
Because the linear factor is cubed: \(12^3=1728\).
Card 16 of 20
MediumStudy card 16
Prompt
What are the side lengths of an unrolled cylindrical tube?
Answer
Cylinder height h and base circumference C.
Card 17 of 20
HardStudy card 17
Prompt
Radius doubles and height halves. What is the cylinder-volume factor?
Answer
2, because \(2^2(1/2)=2\).
Card 18 of 20
HardStudy card 18
Prompt
What equation models water-level rise Δh in a cylinder?
Answer
\(V_{\text{added}}=\pi r^2\Delta h\).
Card 19 of 20
HardStudy card 19
Prompt
What surface is omitted when a hemisphere is joined to a cylinder?
Answer
The shared circular contact surface, because it is internal.
Card 20 of 20
HardStudy card 20
Prompt
What is the most common radius trap?
Answer
Using a supplied diameter or circumference directly as r instead of converting first.
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