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.
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
1 answer
1 answer