Question

The jars A to D are of equal radius. The option which gives the correct relationship among the capacity of jars is:

• A. A = B < C < D
• B. D > B = A = C
• C. B = D > A < C
• D. D > A = B > C

Hint:

A slanted-top jar's capacity depends on the average of its two rim heights, not just the taller wall; compare that average across the four jars in the figure.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Each jar in the figure is a cylindrical jar of the same radius, but the top of each jar is cut off along a slanted straight line instead of a flat horizontal rim. We must rank the four jars by how much liquid they can hold.

Step 2: Key Formula or Approach:
When a cylindrical jar of radius r is cut by a flat slanted plane so that the two opposite sides of the rim sit at heights \(h_1\) and \(h_2\), the capacity of the jar equals the base area times the average of the two rim heights:
\[ V = \pi r^2 \cdot \frac{h_1+h_2}{2} \]
This is because the slanted cut removes a wedge of liquid from one side and that missing wedge is exactly balanced by the extra height on the other side, so the average height gives the true capacity. Since all four jars share the same radius, we only need to compare the average of the two rim heights for each jar.

Step 3: Detailed Explanation:
Reading the figure, jar A has one rim cut all the way down to the base, while the other wall stays at the full height. So its average height is half of the full wall height.
Jar B is cut the same way as jar A, with one rim reaching all the way down to the base and the other rim at the same full height, just drawn with the cut on the opposite side. Since the two rim heights are the same pair of values as jar A, jar B's average height, and so its capacity, comes out equal to jar A's. This gives A = B.
Jar D is cut with a much shorter slanted edge, so its lower rim does not drop all the way to the base, it stays well above zero. That makes the average of jar D's two rim heights bigger than the average for jar A or jar B, so jar D holds more than both, D > A and D > B.
Jar C is drawn as a shorter jar overall, with a small step cut near the top instead of a long slanted cut. Even though the cut in jar C removes less material than the long diagonal cuts in A, B, and D, jar C's walls are shorter to begin with, so its average height, and its capacity, ends up the smallest of the four.
Putting these together: D is the largest, A and B are equal and come next, and C is the smallest.

Step 4: Final Answer:
The capacities satisfy D > A = B > C. \[ \boxed{D > A = B > C} \]