Card 1 of 20
EasyStudy card 1
Prompt
What is pyramid volume?
Answer
\(V=\tfrac13Bh\).
MathChapter 20: Surface Areas and Volumes
Flashcards
Pyramids and Cones Flashcards
Twenty concise cards on pyramid and cone formulas, height distinctions, similar cuts, composites, rates, and scaling.
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Card 2 of 20
EasyStudy card 2
Prompt
What is right-pyramid lateral area?
Answer
\(LA=\tfrac12Pℓ\).
Card 3 of 20
EasyStudy card 3
Prompt
What is total area of a right pyramid?
Answer
\(SA=\tfrac12Pℓ+B\).
Card 4 of 20
EasyStudy card 4
Prompt
What is cone volume?
Answer
\(V=\tfrac13πr²h\).
Card 5 of 20
EasyStudy card 5
Prompt
What is cone lateral area?
Answer
\(LA=πrℓ\).
Card 6 of 20
EasyStudy card 6
Prompt
What is total area of a closed cone?
Answer
\(SA=πrℓ+πr²\).
Card 7 of 20
EasyStudy card 7
Prompt
How are r, h, and ℓ related in a right cone?
Answer
\(ℓ²=r²+h²\).
Card 8 of 20
MediumStudy card 8
Prompt
Which height belongs in pyramid or cone volume?
Answer
The perpendicular height h.
Card 9 of 20
MediumStudy card 9
Prompt
Which height belongs in pyramid or cone lateral area?
Answer
The slant height ℓ.
Card 10 of 20
MediumStudy card 10
Prompt
How does a pyramid's volume compare with a prism sharing B and h?
Answer
The pyramid has one third of the prism's volume.
Card 11 of 20
MediumStudy card 11
Prompt
How does a cone's volume compare with a cylinder sharing r and h?
Answer
The cone has one third of the cylinder's volume.
Card 12 of 20
MediumStudy card 12
Prompt
How do you find a frustum's volume?
Answer
Subtract the removed small cone from the original full cone.
Card 13 of 20
MediumStudy card 13
Prompt
What does a plane parallel to a cone's base create?
Answer
A smaller cone similar to the full cone and a remaining frustum.
Card 14 of 20
MediumStudy card 14
Prompt
A similar cone has linear factor k. What is its volume factor?
Answer
\(k³\).
Card 15 of 20
MediumStudy card 15
Prompt
A similar cone has linear factor k. What is its area factor?
Answer
\(k²\).
Card 16 of 20
MediumStudy card 16
Prompt
How is radius recovered from circumference C?
Answer
\(r=C/(2π)\).
Card 17 of 20
HardStudy card 17
Prompt
What area does an open cone such as a paper hat use?
Answer
Lateral area πrℓ only; do not add a circular base.
Card 18 of 20
HardStudy card 18
Prompt
How is fill time found from a constant volume rate q?
Answer
Divide the container's total volume by q.
Card 19 of 20
HardStudy card 19
Prompt
All cone lengths double. What happens to area and volume?
Answer
Area becomes 4 times as large; volume becomes 8 times as large.
Card 20 of 20
HardStudy card 20
Prompt
What is the one-third-factor trap?
Answer
Using 1/3 in surface area; it belongs only in pyramid and cone volume.
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