Question

If the radius of a cylinder doubles, its volume is __ ^2 or ___ times bigger

If the radius of a cylinder triples, its volume is ___ ^2 or __ times bigger

Answer 1

The volume \( V \) of a cylinder is given by the formula:

\[
V = \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

1. **If the radius of a cylinder doubles (r becomes 2r):**

The new volume \( V' \) is:

\[
V' = \pi (2r)^2 h = \pi (4r^2) h = 4 \pi r^2 h = 4V
\]

So, if the radius of a cylinder doubles, its volume is \( 4 \) times bigger (or \( 4^1 \)).

2. **If the radius of a cylinder triples (r becomes 3r):**

The new volume \( V'' \) is:

\[
V'' = \pi (3r)^2 h = \pi (9r^2) h = 9 \pi r^2 h = 9V
\]

So, if the radius of a cylinder triples, its volume is \( 9 \) times bigger (or \( 9^1 \)).

In summary:

- If the radius of a cylinder doubles, its volume is \( 4^1 \) or \( 4 \) times bigger.
- If the radius of a cylinder triples, its volume is \( 9^1 \) or \( 9 \) times bigger.