Fig.1 and Fig.2 show development views of solids.
The development view of Fig.1 consists of one rectangle, two equilateral triangles, and two trapezoids.
The development view of Fig.2 consists of four equilateral triangles.
Find the volume ratio of the solid made by assembling Fig.1 and the solid made by assembling Fig.2.
The development view of Fig.1 consists of one rectangle, two equilateral triangles, and two trapezoids.
The development view of Fig.2 consists of four equilateral triangles.
Find the volume ratio of the solid made by assembling Fig.1 and the solid made by assembling Fig.2.
Answer
13 : 1
Solution
Fig.3 is the solid made by assembling Fig.1.
Fig.4 is the solid made by assembling Fig.2.
The area of the shadow portion in the figure is set to A cm2.
The volume of Fig.3 is A × (40 + 40 + 50) / 3 = A × 130/3.
The volume of Fig.4 is A × 5 × 1/3 × 2 = A × 10/3.
Therefore the volume ratio of Fig.3 and Fig.4 is 130/3 : 10/3 =13 : 1.
