A cone has a volume of 300 units \( ^{3} \), and a cylinder as a volume of 100 units \( ^{3} \). Is it possible that the cylinder and cone have the same height and the same radius? A Yes, because a cylinder has a volume that is \( 1 / 3 \) the volume of a cone when they are the same height and have the same radius. B No, because a cylinder has a volume that is \( 1 / 3 \) the volume of a cone when they are the same height and have the same radius. C Yes, because a cone has a volume that is \( 1 / 3 \) the volume of a cylinder when they are the same height and have the same radius. D No, because a cone has a volume that is \( 1 / 3 \) the volume of a cylinder when they are the same height and have the same radius.
Upstudy AI Solution
Answer
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Answered by UpStudy AI and reviewed by a Professional Tutor
The Deep Dive
Let's dive into the world of geometry! The volume formula for a cone is \( V = \frac{1}{3} \pi r^2 h \) and for a cylinder, it's \( V = \pi r^2 h \). This means that a cone's volume is indeed one-third that of a cylinder with the same height and radius. Since the cone has a volume of 300 units³ and the cylinder has 100 units³, they can't possibly have the same dimensions. Now, who doesn’t love a good misconception? Picture this: You’ve got a cone and a cylinder, both at a party called “Same Height and Radius.” But the cone insists on being three times the height of the volume comparison! So, the answer is a resounding "No," as the cone can only hold a fraction of what the cylinder can under the same conditions!
