Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
7 because volume of a cylinder is pi r^2 h, and a cone is 1/3 pi r^2 h, which is basically 21 divided by 3??
It was right :)
To find the volume of a cone that fits perfectly inside the soda can, we need to follow these steps:
Step 1: Determine the radius of the soda can.
Since the diameter of the soda can is given as 6, we can calculate the radius by dividing the diameter by 2.
Radius = Diameter / 2 = 6 / 2 = 3.
Step 2: Calculate the volume of the soda can.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Here, the volume of the soda can is given as 21.
Step 3: Calculate the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the height of the cone is the same as the height of the soda can, so we can use the same value. The radius of the cone is also the same as the radius of the soda can. Therefore, the volume of the cone is (1/3) times the volume of the soda can.
Step 4: Calculate the volume of the cone.
Volume of cone = (1/3) * Volume of soda can
Volume of cone = (1/3) * 21
Volume of cone = 7.
Therefore, the volume of the cone that fits perfectly inside the soda can is 7.
To find the volume of a cone that fits perfectly inside a soda can, first, let's find the height of the cone.
Since the diameter of the soda can is given as 6, the radius of the soda can is half of the diameter, which is 6/2 = 3.
The cone that fits perfectly inside the soda can will have the same height as the soda can. However, the height of the soda can is not provided in the question.
Therefore, to find the height of the cone, we need to use the volume formula for a cylinder.
The volume formula for a cylinder is V = πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
In this case, the volume of the soda can is given as 21 and the radius is 3.
Plugging these values into the formula, we get 21 = π(3^2)h.
Simplifying this equation, we have 21 = 9πh.
Now, divide both sides of the equation by 9π:
21 / 9π = h.
To find the value of h, we can use a calculator to do the division:
h ≈ 0.7854 (approximately).
Now that we have the height of the cone, we can find its volume.
The volume formula for a cone is V = (1/3)πr^2h.
Since the radius of the soda can is 3, the radius of the cone is also 3.
Plugging these values into the formula, we have:
V = (1/3)π(3^2)(0.7854).
Simplifying this equation, we get:
V ≈ 7.0686.
Thus, the volume of the cone that fits perfectly inside the soda can is approximately 7.0686.