Solve both parts and justify the conditions used. Part A: How many planes contain two distinct parallel lines? Explain. Part B: A cone has radius r and height h. Write its volume as cπ and find c.

01 / Standard#Your turn

\begin{gathered}\text{B: }r=9,\quad h=3\end{gathered}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A: Use precise incidence conditions; diagrams alone do not prove spatial relationships.

Hint 2

B: Choose the correct surface or volume formula and keep units and similarity powers consistent.

Worked solution

Part A reasoning
Use precise incidence conditions; diagrams alone do not prove spatial relationships.
Calculate or simplify this relation.
$l\parallel m,\ l\ne m\Rightarrow\exists!\alpha:l,m\subseteq\alpha$
The three selected points are noncollinear and determine a unique plane.
Part B reasoning
Choose the correct surface or volume formula and keep units and similarity powers consistent.
Calculate or simplify this relation.
$V=\frac13\pi r^2h=81\pi$
Do not omit the factor one third.

A: The requested value is 1. B: The requested value is 81.

Checks and common pitfalls: The three selected points are noncollinear and determine a unique plane. Do not omit the factor one third.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Introduction to solid geometry: mixed assessment