Find the volume of a right circular cone with base diameter 12.0 m and slant height is 10.0m . Round to the nearest whole
r = 6
base area = pi (36)
height = sqrt (100 -36) = 8
vol = (1/3) pi (36)(8)
To find the volume of a right circular cone, we can use the formula:
Volume = (1/3) * π * r^2 * h,
where π is a constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.
First, we need to determine the radius of the base. The base diameter is given as 12.0 m, which means the radius is half of the diameter, so:
Radius = 12.0 m / 2 = 6.0 m.
Next, we need to find the height of the cone. The slant height is given as 10.0 m, and with the Pythagorean theorem, we can find the height (h) using the following equation:
h^2 = slant height^2 - radius^2.
Plugging in the given values:
h^2 = (10.0 m)^2 - (6.0 m)^2
= 100 m^2 - 36 m^2
= 64 m^2.
To solve for the height, we take the square root:
h = √(64 m^2)
= 8 m.
Now, we have the radius (r = 6.0 m) and height (h = 8 m). Plugging these values into the volume formula:
Volume = (1/3) * π * (6.0 m)^2 * 8 m
≈ 3.14159 * 36 m^2 * 8 m / 3
≈ 3.14159 * 288 m^3 / 3
≈ 904.77792 m^3.
Rounding to the nearest whole number, the volume of the right circular cone is approximately 905 m^3.