First, let's examine each statement one by one and determine if it is true or false.
1. The radius of the cone is 9 units.
- Given: The radius is indeed 9 units.
- Conclusion: This statement is true.
2. The height of the cone is 15 units.
- Given: One height of the cone is 15 units.
- Conclusion: This statement is true.
3. The height of the cone is 12 units.
- Given: Another height of the cone is 12 units.
- Conclusion: This statement is true.
4. The volume of the cone is represented by the expression [tex]$\frac{1}{3} \pi(15)^2(9)$[/tex].
- We need to check if for the radius 9 and height 15, the volume matches the given expression.
- The volume formula for a cone is [tex]\( V = \frac{1}{3} \pi r^2 h \)[/tex], and substituting in our radius and height would give us:
[tex]\[
V = \frac{1}{3} \pi (9)^2 (15)
\][/tex]
- The given expression is [tex]\(\frac{1}{3} \pi (15)^2 (9)\)[/tex].
- Comparing both expressions, ours has [tex]\((9)^2 \cdot 15\)[/tex] while the given expression has [tex]\((15)^2 \cdot 9\)[/tex].
- [tex]\( (9)^2 = 81 \)[/tex] and [tex]\( (15)^2 = 225 \)[/tex], these are not the same.
- Conclusion: This statement is false.
5. The volume of the cone is represented by the expression [tex]$\frac{1}{3} \pi (9)^2 (12)$[/tex].
- We need to check if for the radius 9 and height 12, the volume matches the given expression.
- Substituting in our radius and height into the volume formula would give us:
[tex]\[
V = \frac{1}{3} \pi (9)^2 (12)
\][/tex]
- The given expression is [tex]\(\frac{1}{3} \pi (9)^2 (12)\)[/tex], which matches exactly.
- Conclusion: This statement is true.
Thus, the statements that are true are:
1. The radius of the cone is 9 units.
2. The height of the cone is 15 units.
3. The height of the cone is 12 units.
5. The volume of the cone is represented by the expression [tex]$\frac{1}{3} \pi (9)^2 (12)$[/tex].
