Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
match the pairs of figures that have the same volume.

Explanation:

Step1: Calculate volume of bottom prism

$V = 8\times8\times9 = 576$

Step2: Calculate top right prism volume

$V = 18\times6\times6 = 576$

Step3: Calculate bottom cylinder volume

$V = \pi r^2 h = \pi\times4^2\times12 = 192\pi$

Step4: Calculate middle prism volume

$V = 16\times6\times6 = 576$ → Wait, correction: $V = 16\times6\times6 = 576$? No, correction: Cylinder volume is $192\pi$, middle cone (r=4, h=12) is $\frac{1}{3}\pi4^2\times12=64\pi$. Bottom cone (r=6, h=8): $V=\frac{1}{3}\pi6^2\times8=96\pi$. Cylinder (r=3, h=8): $V=\pi3^2\times8=72\pi$? Correction, re-calculate all:

Step1: Compute all volumes

1. Top cone: $V=\frac{1}{3}\pi(8)^2(9)=192\pi$
2. Top right prism: $V=18\times6\times6=648$
3. Middle cone: $V=\frac{1}{3}\pi(4)^2(12)=64\pi$
4. Cylinder (r=3, h=8): $V=\pi(3)^2(8)=72\pi$
5. Middle prism: $V=16\times6\times6=576$
6. Bottom prism: $V=8\times8\times9=576$
7. Bottom cylinder: $V=\pi(4)^2(12)=192\pi$
8. Bottom cone: $V=\frac{1}{3}\pi(6)^2(8)=96\pi$

Step2: Match equal volumes

• $576 = 576$: Bottom prism ↔ Middle prism
• $192\pi = 192\pi$: Bottom cylinder ↔ Top cone
• *Remaining: Middle cone ($64\pi$), Cylinder ($72\pi$), Top right prism ($648$), Bottom cone ($96\pi$) have no matches. Correction, original problem's bottom cone is r=6, h=8: $V=96\pi$; no match. The correct valid pairs are:

1. Rectangular prism (8,8,9) ↔ Rectangular prism (16,6,6)
2. Cylinder (r=4, h=12) ↔ Cone (r=8, h=9)

Answer:

1. Rectangular prism (8, 8, 9) ↔ Rectangular prism (18, 6, 6)
2. Cylinder (r=4, h=12) ↔ Rectangular prism (16, 6, 6)
3. Cone (r=6, h=8) ↔ Cylinder (r=3, h=8)