Answer:
Formula for the volume of the cylinder is given by;
where r is the radius of the cylinder and h be the height of the cylinder.
As per the statement:
Volume of cylinder(V) = 364.5 cubic inches.
You will cut its bottom from a square of metal and form its curved side by bending a rectangular sheet of metal.
Diameter of a circle = 2r
Then, side of the square (s) = 2r
Area of a square = square inches.
Since, Volume of the cylinder(V) =
then;
Substitute the value of V then we have
To find the total amount of material required for the square and the rectangle in terms of r.
Curved surface area of cylinder =
Substitute the value of h we have;
Curved surface area of cylinder =
= square inches.
then;
= square inches
Therefore, the total amount of material required for the square and the rectangle in terms of r is, square inches