what is the volume of the cone, rounded to the nearest cubic inch?
A cone with height 6 in. and diameter 12 in.
To calculate the volume of a cone, you can use the formula V = (1/3)πr^2h, where V is the volume, π is pi (approximately 3.14159), r is the radius, and h is the height.
Given that the diameter is 12 inches, we can find the radius by dividing it by 2:
radius = diameter / 2 = 12 in / 2 = 6 in.
Now we have all the necessary values to calculate the volume:
V = (1/3)πr^2h = (1/3) * 3.14159 * 6^2 * 6 = 3.14159 * 6^3 = 3.14159 * 216 = 678.58464 cubic inches.
Rounding this to the nearest cubic inch gives us a volume of approximately 679 cubic inches.
To find the volume of a cone, you can use the following formula:
V = (1/3) * π * r^2 * h
where V represents the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height.
Firstly, we need to find the radius of the cone. The diameter (d) is given as 12 inches, and the relationship between radius and diameter is r = d/2. Therefore, the radius (r) is 12/2 = 6 inches.
Using the formula, substitute the known values:
V = (1/3) * 3.14159 * 6^2 * 6
V = (1/3) * 3.14159 * 36 * 6
V = 3.14159 * 6 * 12
V ≈ 226.195 cubic inches
Rounded to the nearest cubic inch, the volume of the cone is approximately 226 cubic inches.
The radius of the cone is half of the diameter, so it is 6 inches.
Using the formula for the volume of a cone:
V = (1/3)πr^2h
V = (1/3)π(6^2)(6)
V = 113.1 cubic inches
Rounded to the nearest cubic inch, the volume of the cone is approximately 113 cubic inches.