The volume of a cone that fits exactly inside a cylinder is 20 cubic feet. What is the volume of the cylinder? (5 points) Select one:
a. 4 cubic feet
b. 5 cubic feet
c. 40 cubic feet
d. 60 cubic feet
IDK WHAT TO DO!!!
You need to know your cones.
The volume of a cone is 1/3 the volume of the cylinder it would be enclosed in.
Vcone=1/2 PI*radius^2 * height
It is more broad than that. The volume of any right Pyramid (including cones) is 1/3 the volume of the right prism that encloses it.
VolumePyramid= 1/3 basearea*height
Math is really awesome.
67
To find the volume of the cylinder, we need to use the information given about the cone. Here's how you can solve this problem step by step:
Step 1: Understand the relationship between the cone and the cylinder.
In this case, the cone is completely enclosed inside the cylinder, which means the diameter and height of the cone are equal to the diameter and height of the cylinder.
Step 2: Recall the formula for the volume of a cone.
The volume of a cone can be calculated using the formula: V_c = (1/3) * π * r_c^2 * h_c, where V_c is the volume of the cone, r_c is the radius of the cone, and h_c is the height of the cone.
Step 3: Assume the radius and height of the cone.
Since we are given the volume of the cone (20 cubic feet), we can assume any radius and height that fits the volume condition.
Let's assume the radius of the cone (r_c) is 1 foot and the height of the cone (h_c) is 6 feet. So, the volume of the cone would be:
V_c = (1/3) * π * (1^2) * 6
= (1/3) * π * 1 * 6
= 2 * π
Step 4: Determine the volume of the cylinder using the cone's volume.
The volume of the cylinder is equal to the volume of the cone since the cone completely fits inside the cylinder. So, the volume of the cylinder is also 20 cubic feet.
Now, looking at the given answer options:
a. 4 cubic feet
b. 5 cubic feet
c. 40 cubic feet
d. 60 cubic feet
The correct answer is c. 40 cubic feet since that's the option that matches the calculated volume of the cylinder.
Remember, in math problems like these, it is crucial to consider multiple factors and assumptions to arrive at a solution.