There is a square pyramid with a square In the bottom and an isosceles triangle in the side as shown in Fig. 1.
The intersection of AC and BD is set to O.
When O is connected to the vertex P, PO will become vertical to AC and BD, respectively.
The point in the middle of PO is set to M.
The intersection of the extension of CM and the side PA is set to E.
Moreover, the point which divides the side PB into 3 : 1 is set to F.
The intersection of the plane EPC and side PD is set to G.
Three point G, M, and F are located on a straight line.
Answer the following questions at this time.
The ratio should be by the least integer.
(1) With reference to Fig. 2 and find PE : EA.
(2) With reference to Fig. 3 and find PG : GD.
(3) Find the ratio of the volume of triangular pyramid P-ECG to the volume of square pyramid P-ABCD.
(4) Cut the square pyramid P-ABCD with Plane EFCG.
The volume of the upper solid is set to U and the lower solid is set to V.
Find the ratio of U to V at this time.
The intersection of AC and BD is set to O.
When O is connected to the vertex P, PO will become vertical to AC and BD, respectively.
The point in the middle of PO is set to M.
The intersection of the extension of CM and the side PA is set to E.
Moreover, the point which divides the side PB into 3 : 1 is set to F.
The intersection of the plane EPC and side PD is set to G.
Three point G, M, and F are located on a straight line.
Answer the following questions at this time.
The ratio should be by the least integer.
(1) With reference to Fig. 2 and find PE : EA.
(2) With reference to Fig. 3 and find PG : GD.
(3) Find the ratio of the volume of triangular pyramid P-ECG to the volume of square pyramid P-ABCD.
(4) Cut the square pyramid P-ABCD with Plane EFCG.
The volume of the upper solid is set to U and the lower solid is set to V.
Find the ratio of U to V at this time.
Answer
(1) 1 : 2
(2) 3 : 5
(3) 1 : 16
(4) 3 : 13
(2) 3 : 5
(3) 1 : 16
(4) 3 : 13
Reference
