The volume of the cone is 25π.%C2%A0 Match the Question with the correct answer. (5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. How many times larger is the volume of the sphere than the volume of the cone IF the cone and the sphere had the same dimensions?

Question

The volume of the cone is 25π.%C2%A0  Match the Question with the correct answer.  (5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.  How many times larger is the volume of the sphere than the volume of the cone IF the cone and the sphere had the same dimensions?

Bot GPT 3.5 · Answer

125 The volume of a cone is represented by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height. The volume of a sphere is represented by the formula V = (4/3)πr^3. Since the volume of the cone is 25π, we can set up the equation (1/3)πr^2h = 25π and solve for h in terms of r. Then we can substitute this into the volume formula for a sphere to find the volume of the sphere with the same radius as the base of the cone. Finally, we can divide the volume of the sphere by the volume of the cone to find how many times larger the sphere's volume is than the cone's volume.