The figure below is a solid which is made by hollowing out the cylinder whose diameter of the bottom is 2cm and height is 4cm from the cube whose length of one side is 4cm.
Each center of the bottoms of the hollowed cylinder is the same as the diagonal of the intersection of square ABCD and square EFGH respectively.
Point M is a middle point of the side CG.
This solid is cut by the plane that passes three points E, F and M.
Find the volume of the solid including face ABCD.
Pi is set to be 3.14.
Answer
38.58 cm3
Solution
The volume of the solid ABCD-EFMN is 4 × 4 × 4 × 3/4 = 48 cm3.
PS = 4 - ( 2 × 1/4) = 7/2 cm.
QR = 4 - ( 2 × 3/4) = 5/2 cm.
The volume of the below part of cylinder is 1 × 1 × 3.14 × (7/2 + 5/2) × 1/2 = 9.42 cm3 .
Therefore the volume to be found is 48 - 9.42 = 38.58 cm3.
