Michael, Charlotte, and Kai went to a movie theater that sells popcorn in cone-shaped containers. Each container has a diameter of 8 inches and a height of 10 inches. If they each buy a container, how many cubic inches of popcorn will they have in total? Round to the nearest tenth.
A) 251.2 in3
B) 502.4 in3
C) 83.7 in3
D) 167.5 in3
The formula to calculate the volume of a cone is (1/3)πr²h, where r is the radius and h is the height.
The radius of the container is half of the diameter, so it is 8 inches / 2 = 4 inches.
Using the formula, the volume of one container is (1/3)π(4 inches)²(10 inches) = (1/3)π(16 inches²)(10 inches) = (1/3)(3.14)(16 inches²)(10 inches) = (1/3)(3.14)(160 inches²) = (1.047)(160 inches²) = 167.35 inches³.
Since there are three people buying one container each, the total volume of popcorn is 3 * 167.35 inches³ = 502.05 inches³.
Rounded to the nearest tenth, the answer is approximately 502.1 inches³.
Therefore, the correct option is:
A) 251.2 in³