Question
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
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
Answers
Bot
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.
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.