Final answer:
To find the volume of the cone, calculate the radius and height of the cone using the given measurements. Then, use the formula for the volume of a cone to find the answer.
Step-by-step explanation:
To find the volume of the cone, we need to find the radius and height of the cone. The radius of the circular paper is given as 5 cm, and the sector cut out has an angle of 30°. Since the sector is a portion of a circle, we can find its radius by multiplying the radius of the circular paper by the fraction of the angle it covers, which is 30°/360°. So the radius of the sector is 5 cm * (30°/360°) = 0.4167 cm.
Now, let's find the circumference of the sector. The circumference of the sector is equal to the circumference of the base of the cone. We can find the circumference of the sector by multiplying the radius of the sector by 2π. So the circumference of the sector is 2π * 0.4167 cm ≈ 2.618 cm.
Next, we need to find the height of the cone. The height of the sector is equal to the slant height of the cone. We can use the Pythagorean theorem to find the slant height. The slant height is the hypotenuse of a right triangle with the radius of the sector as one of the legs, and the height of the sector as the other leg. We can find the height of the sector by using the formula h = r * sin(θ), where r is the radius of the sector and θ is the angle of the sector. So the height of the sector is 0.4167 cm * sin(30°) ≈ 0.2083 cm.
Finally, we can find the volume of the cone using the formula: Volume = (1/3) * π * r^2 * h. Plugging in the values we found, the volume of the cone is (1/3) * π * 0.4167^2 * 0.2083 ≈ 0.0110 cm^3.
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