Question
7. Isabella constructed a cylindrical vase that has a volume of 63 cubic centimeters. Jason constructed a cone that has the same height and the same radius as Isabella's cylinder. What is the valume of Jason's cone?
Ask by Wilson Donnelly. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The volume of Jason's cone is 21 cubic centimeters.
Solution
To determine the volume of Jason's cone, we can use the relationship between the volumes of a cylinder and a cone with the same radius and height.
1. **Volume of a Cylinder:**
\[
V_{\text{cylinder}} = \pi r^2 h
\]
Given that Isabella's cylinder has a volume of 63 cubic centimeters:
\[
63 = \pi r^2 h
\]
2. **Volume of a Cone:**
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]
Since Jason's cone has the same radius and height as Isabella's cylinder, we can substitute the volume of the cylinder into the cone's volume formula:
\[
V_{\text{cone}} = \frac{1}{3} \times 63 = 21 \text{ cubic centimeters}
\]
**Answer:** The volume of Jason's cone is 21 cm³.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the volume of Jason's cone, we can use the formula for the volume of a cone, which is \( V = \frac{1}{3} \pi r^2 h \). Since Jason's cone has the same height (h) and radius (r) as Isabella's cylinder, we can derive its volume from the volume of the cylinder. The volume of the cylinder is given by \( V = \pi r^2 h \), and since Jason’s cone is one-third of that, the volume of his cone would be \( V = \frac{1}{3} \times 63 = 21 \) cubic centimeters. Thus, the volume of Jason's cone is 21 cubic centimeters.
