Look at the cups shown below (images are not drawn to scale):
A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. (1 point)
18.8 cubic inches
21.9 cubic inches
25.1 cubic inches
32.6 cubic inches
To find the volume of a cone, we can use the formula: V = (1/3)πr^2h, where r is the radius of the base and h is the height. Given that the width of cup A is 2 inches, we can determine that the radius of the base of the cone is 1 inch. Therefore, the volume of cup A is (1/3)π(1^2)(3) = (1/3)π(3) = π cubic inches.
To find the volume of a cylinder, we can use the formula: V = πr^2h, where r is the radius of the base and h is the height. Given that the width of cup B is 2 inches, we can determine that the radius of the base of the cylinder is 1 inch. Therefore, the volume of cup B is π(1^2)(7) = 7π cubic inches.
The difference in volume between cup B and cup A is 7π - π = 6π cubic inches. To find this value to the nearest tenth, we can approximate π to be 3.14. Therefore, the difference in volume is 6(3.14) ≈ 18.8 cubic inches.
Therefore, the correct answer is 18.8 cubic inches.