- Start at the yellow box labeled "Start!" with the pyramid (base 8m x 9m, height 9m). Volume = (1/3) * 8 * 9 * 9 = 216 m³. The correct path is to the box labeled 270 m³ (next to the triangular prism with base 14m, 14m, 20m and height 14m: Volume = (1/2)*14*14*20 = 1960? Wait, that doesn't match. Let me recalculate all volumes properly based on standard formulas and the given dimensions.
Actually, let's verify each step by calculating the volume for each shape along the path:
1.
Start: Pyramid with rectangular base 8m x 9m, height 9m.
Volume = (1/3) * base area * height = (1/3) * (8 * 9) * 9 = (1/3) * 72 * 9 = 216 m³.
The box next to it labeled 270 m³ is incorrect for this shape. Looking at the maze, the start box is connected to several others. The label "270 m³" is in a box below the start. Let's check the shape in that box: It appears to be a triangular prism with base triangle sides 14m, 14m, 20m? That seems odd. Actually, looking again, the box labeled "270 m³" contains a triangular prism with base 14m, 14m, and height 14m? That doesn't make sense. Perhaps the dimensions are for the triangular base and the length of the prism.
Wait, let's look at the box directly to the right of "Start!". It has a cone with radius 7m and height 18m.
Volume = (1/3) * π * r² * h ≈ (1/3) * 3.1416 * 49 * 18 ≈ (1/3) * 3.1416 * 882 ≈ 3.1416 * 294 ≈ 923.6 m³. This matches the label "923.6 m³".
So the path from Start goes to the cone (923.6 m³).
2. From the cone (923.6 m³), the path goes to the box labeled "End!" which is directly to the right. The "End!" box is connected to the cone and also to a box labeled "112 m³" (which is a rectangular prism 7m x 4m x 4m: 7*4*4=112 m³). But the direct path from the cone to "End!" is valid.
Therefore, the solution path is:
Start → Cone (923.6 m³) → End!
The volumes along the path are:
- Start (Pyramid): 216 m³ (calculated, but not labeled on the path)
- Cone: 923.6 m³
- End!
Parent Tip: Review the logic above to help your child master the concept of volume of pyramids and cones worksheet answers.
