To determine whether the statement is true or false, let's analyze the volumes of a cone and a cylinder with the same base (radius) and height (altitude).
1. Volume of a Cylinder:
- The formula for the volume of a cylinder is given by:
[tex]\[
V_{\text{cylinder}} = \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cylinder.
2. Volume of a Cone:
- The formula for the volume of a cone is given by:
[tex]\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cone.
3. Comparison:
- We notice from the formulas that the volume of a cone is:
[tex]\[
V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}}
\][/tex]
- This implies that the volume of a cone is one-third the volume of a cylinder when both have the same base radius and height.
Based on this analysis, the statement "A cone has one-third times the volume of a cylinder with the same base and altitude" is indeed correct.
Therefore, the correct answer is:
OA. True.
