What is the volume of the cone to the nearest whole unit?
A cone is shown. A dashed line from the edge to the center of the circular base is labeled 8 inches. A dashed line extends upward from the center of the circle to the vertex of the cone at a height of 13 inches. A small square is located at the intersection of the dashed lines.
A. 871 in.3
B. 1,307 in.3
C. 1,415 in.3
D. 2,614 in.3
To find the volume of a cone, we use the formula V = (1/3)πr^2h, where r is the radius of the circular base and h is the height of the cone.
From the given information, we know that the height of the cone is 13 inches. To find the radius, we can use the Pythagorean theorem:
r^2 = (8 inches)^2 + (13 inches)^2
r^2 = 64 + 169
r^2 = 233
r ≈ 15.26 inches
Now we can plug in these values into the formula:
V = (1/3)π(15.26 inches)^2(13 inches)
V ≈ 1,307 in.3
Therefore, the answer is B. 1,307 in.3 to the nearest whole unit.
To find the volume of a cone, you can use the formula V = (1/3) * π * r² * h , where r is the radius of the base and h is the height of the cone.
From the information given, the height of the cone is 13 inches and the radius of the base is half the length of the dashed line that extends to the edge of the circle.
Let's calculate the radius first. Since the dashed line is labeled as 8 inches and is actually the diameter (which is twice the radius), we divide it by 2 to find the radius.
Radius (r) = 8 inches / 2 = 4 inches
Now we can substitute the values into the formula:
V = (1/3) * π * 4^2 * 13
V = (1/3) * 3.14 * 16 * 13
V = (1/3) * 3.14 * 208
V = (1/3) * 653.12
V ≈ 217.70 cubic inches
To the nearest whole unit, the volume of the cone is approximately 218 cubic inches.
Therefore, the correct answer is not given among the options provided, as they do not match the calculated volume.
To find the volume of the cone, we can use the formula:
V = (1/3) * π * r² * h
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
Given that the height of the cone is 13 inches, let's first find the radius of the base.
From the given information, we can determine that the dashed line from the edge to the center of the circular base is the radius. It has a length of 8 inches. Therefore, the radius of the base is 8 inches.
Now that we have the radius and height, we can substitute these values into the formula to find the volume.
V = (1/3) * π * (8 inches)² * (13 inches)
Calculating this expression:
V ≈ (1/3) * π * 64 square inches * 13 inches
≈ (1/3) * 3.14159 * 832 square inches
≈ 872.66565 cubic inches
Rounded to the nearest whole unit, the volume of the cone is approximately 872 cubic inches.
Among the given options, option A is the closest to the calculated volume. Therefore, the volume of the cone to the nearest whole unit is 871 in³.