A solid metal prism has a rectangle base with sides of 4 inches and a height of 4inches a hole in the shape of a cylinder with a radius of 1 inch is drilled trough the entire length of the rectangular prism

77 cubic inches

Step-by-step explanation:

Here is the complete question.

A solid metal prism has a rectangle base with sides of 4 inches and 6 inches and a height of 4 inches . A hole in the shape of a cylinder with a radius of 1 inch is drilled trough the entire length of the rectangular prism. What is the approximate volume of the remaining solid in cubic inches.

Solution

The volume of the solid prism is given by V = Area of base × height = lbh = 4 × 6 × 4 = 96 cubic inches.

The volume of the cylindrical hole is given by πr²h

r = 1 inch and h = 6 inches. So V = πr²h = π × 1² × 6 = 18.85 cubic inches.

The volume of the remaining solid = volume of solid prism - volume of cylindrical hole = (96 - 18.85) cubic inches = 77.15 cubic inches ≅ 77 cubic inches