A cone has a height of 5 inches and a circumference of 56.52 inches.
Which measurement is closest to the volume of the cone in cubic inches? Use 3.14 for 7x5.
a.1695.6
b.1271.7
c.887.36
d.423.9
2πr = 56.52
r = 9
v = 1/3 πr^2h = 1/3 * π * 9^2 * 5 = 423.9
To find the volume of a cone, we use the formula: V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cone.
In this case, we are given the height of the cone, which is 5 inches. However, we are not given the radius of the base directly.
To find the radius, 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 have: r = C / (2 * π).
Given the circumference of the cone, which is 56.52 inches, we can calculate the radius:
r = 56.52 / (2 * 3.14) ≈ 8.99 inches.
Now, we can substitute the values in the volume formula:
V = (1/3) * 3.14 * (8.99)^2 * 5 ≈ 423.915 cubic inches.
Rounded to the nearest whole number, the volume is approximately 424 cubic inches.
Out of the given options, the measurement closest to 424 is option d: 423.9.
Therefore, the answer is option d.
To find the volume of a cone, we need to use the formula: V = (1/3) * π * r^2 * h
Given that the height (h) is 5 inches, and the circumference is 56.52 inches, we can find the radius (r) of the cone using the formula: C = 2πr.
Plugging in the given circumference value, we have:
56.52 = 2πr
Divide both sides of the equation by 2π to solve for r:
r = 56.52 / (2 * π)
r ≈ 9.01 inches (rounded to two decimal places)
Now, we can substitute the values of r and h into the formula for the volume of the cone:
V = (1/3) * π * (9.01)^2 * 5
V ≈ (1/3) * 3.14 * (9.01)^2 * 5
V ≈ 47.12 * 81.081 * 5
V ≈ 19155.93 cubic inches
Among the given options, the measurement closest to the volume of the cone is:
a. 1695.6 (rounded to the nearest tenth)