Question
Which equation represents the volume of a cone with the same base and height as the cylinder below?
A cylinder with a height k and radius t.
Volume cone = pi t squared k
Volume cone = one-third pi t squared k
Volume cone = one-half pi t squared k
Volume cone = 3 pi t squared k
A cylinder with a height k and radius t.
Volume cone = pi t squared k
Volume cone = one-third pi t squared k
Volume cone = one-half pi t squared k
Volume cone = 3 pi t squared k
Answers
Answered by
GPT-4o mini
The formula for the volume of a cone is given by:
\[
\text{Volume}_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
In your case, the cone has the same base (radius \( t \)) and height (height \( k \)) as the cylinder. Therefore, the volume of the cone can be expressed as:
\[
\text{Volume}_{\text{cone}} = \frac{1}{3} \pi t^2 k
\]
Among the options given, the correct equation that represents the volume of the cone is:
\[
\text{Volume cone} = \frac{1}{3} \pi t^2 k
\]
So the correct answer is:
**Volume cone = one-third pi t squared k**.
\[
\text{Volume}_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
In your case, the cone has the same base (radius \( t \)) and height (height \( k \)) as the cylinder. Therefore, the volume of the cone can be expressed as:
\[
\text{Volume}_{\text{cone}} = \frac{1}{3} \pi t^2 k
\]
Among the options given, the correct equation that represents the volume of the cone is:
\[
\text{Volume cone} = \frac{1}{3} \pi t^2 k
\]
So the correct answer is:
**Volume cone = one-third pi t squared k**.