What is the volume of a cone with a diameter of 20 and a height of 15? Use 3.14 for pi
The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
where V is volume, r is the radius of the base of the cone, h is the height, and π is pi.
First, we need to find the radius (r) of the cone. The diameter is given as 20, so the radius will be half of that:
r = diameter / 2 = 20 / 2 = 10
Now we can plug in the values into the formula:
V = (1/3) * π * r^2 * h = (1/3) * 3.14 * (10^2) * 15
Now, calculate the square of the radius (r^2):
r^2 = 10^2 = 100
And continue with the calculation:
V = (1/3) * 3.14 * 100 * 15
V = 3.14 * 100 * 5
V = 314 * 5
V = 1570
So the volume of the cone with a diameter of 20 and a height of 15, using 3.14 for pi, is 1570 cubic units.
When calculating the volume of a cone, you again use the formula:
V = (1/3) * π * r^2 * h
In this case, the radius (r) is given as 5 and the height (h) is given as 9. As before, we'll use π as 3.14.
Plugging the values into the formula, we get:
V = (1/3) * 3.14 * (5^2) * 9
First, square the radius:
5^2 = 25
So the equation becomes:
V = (1/3) * 3.14 * 25 * 9
Now perform the multiplication:
V = 3.14 * 25 * 3
V = 78.5 * 3
V = 235.5
So the volume of the cone with a radius of 5 and a height of 9 is 235.5 cubic units.
To calculate the volume of chocolate needed to fill the cone-shaped mold, we need to use the formula for the volume of a cone, which is:
V = (1/3) * π * r^2 * h
where:
V = volume of the cone
π = pi (approximately 3.14)
r = radius of the base of the cone
h = height of the cone
The diameter of the cone is given as 2 cm, so the radius (r) is half of the diameter:
r = diameter / 2 = 2 cm / 2 = 1 cm
The height (h) of the cone is given as 6 cm.
Plugging these values into the formula, we get:
V = (1/3) * 3.14 * (1 cm)^2 * 6 cm
V = (1/3) * 3.14 * 1 * 6 cm^3
V = (1/3) * 18.84 cm^3
V = 6.28 cm^3
So, the volume of chocolate needed to make a solid chocolate cone with a diameter of 2 cm and a height of 6 cm is 6.28 cubic centimeters.
To find the volume of sand needed to fill the cone-shaped mold, we again use the volume formula for a cone:
V = (1/3) * π * r^2 * h
Given that the mold has a diameter of 4 meters, we first determine the radius, which is half the diameter:
r = diameter / 2 = 4 meters / 2 = 2 meters
Now we have the radius (r = 2 meters) and the height (h = 6 meters). Plugging these into the formula with π as 3.14, we get:
V = (1/3) * 3.14 * (2 meters)^2 * 6 meters
First, square the radius:
(2 meters)^2 = 4 square meters
Now, compute the volume:
V = (1/3) * 3.14 * 4 square meters * 6 meters
V = (1/3) * 3.14 * 24 cubic meters
V = 3.14 * 8 cubic meters
V = 25.12 cubic meters
The volume of sand needed to fill the mold is 25.12 cubic meters.