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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.