Find the volume of a right circular cone that has a height of 17.5 m and a base with a circumference of 19.4 m. Round your answer to the nearest tenth of a cubic meter.
We can start by using the formula for the circumference of a circle to find the radius of the base. The formula is:
C = 2πr
where C is the circumference and r is the radius.
We know that the circumference is 19.4 m, so we can solve for r:
19.4 = 2πr
r = 19.4 / (2π) ≈ 3.09 m
Now we can use the formula for the volume of a right circular cone, which is:
V = (1/3)πr^2h
where V is the volume, r is the radius of the base, and h is the height.
Plugging in the values we have, we get:
V = (1/3)π(3.09^2)(17.5)
V ≈ 56.7 cubic meters
Rounding to the nearest tenth, we get:
V ≈ 56.7 m^3
Therefore, the volume of the cone is approximately 56.7 cubic meters.
To find the volume of a right circular cone, we can use the formula:
V = (1/3) * π * r^2 * h
where V is the volume, π is pi (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
First, we need to find the radius of the base. We know that the circumference of the base is 19.4 m, so we can use the formula for the circumference of a circle:
C = 2 * π * r
where C is the circumference and r is the radius. Rearranging the formula, we can solve for the radius:
r = C / (2 * π) = 19.4 / (2 * 3.14159) ≈ 3.08 m
Now that we have the height (h = 17.5 m) and the radius (r ≈ 3.08 m), we can plug these values into the volume formula:
V = (1/3) * π * (3.08)^2 * 17.5 ≈ 88.4 cubic meters
Therefore, the volume of the right circular cone is approximately 88.4 cubic meters (rounded to the nearest tenth).
To find the volume of a right circular cone, we need to use the formula:
V = (1/3) * π * r^2 * h
where V represents the volume, π is a mathematical constant approximately equal to 3.14159, r represents the radius of the cone's base, and h represents the height of the cone.
In this case, we are given the height of the cone as 17.5 m. To find the radius (r) of the base, we can use the formula to find the circumference of a circle:
C = 2 * π * r
Given that the base has a circumference of 19.4 m, we can rearrange the formula to solve for the radius (r):
r = C / (2 * π)
Substituting the given value for the circumference:
r = 19.4 / (2 * π)
Now that we have the radius (r) and the height (h), we can calculate the volume (V):
V = (1/3) * π * (19.4 / (2 * π))^2 * 17.5
Simplifying the expression:
V = (1/3) * (19.4 / (2 * π))^2 * 17.5
Calculating the value:
V ≈ 15.6 m^3
Therefore, the volume of the right circular cone is approximately 15.6 cubic meters.