Question

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.
a.18.8 cubic inches
b.21.9 cubic inches
c.25.1 cubic inches
d.32.6 cubic inches

Answer 1

Cup B will hold 12.6 more cubic inches of juice than cup A when both are completely full.

Step-by-step explanation:

To find the volume of the cone, we can use the formula V = (1/3)πr²h, where r is the radius and h is the height.

For cup A, the radius is 1 inch and the height is 3 inches. So the volume of cup A is (1/3)π(1 inch)²(3 inches) = (1/3)π(1 inch)²(3 inches) = 3π cubic inches.

For cup B, the radius is also 1 inch, but the height is 7 inches. So the volume of cup B is (1/3)π(1 inch)²(7 inches) = (1/3)π(1 inch)²(7 inches) = 7π cubic inches.

Therefore, cup B will hold 7π - 3π = 4π more cubic inches of juice than cup A.

Using the approximation π ≈ 3.14, we can calculate the difference in volume approximately as 4π ≈ 4(3.14) = 12.56 cubic inches. Rounding to the nearest tenth, the answer is 12.6 cubic inches.