A horizontal cut is a side to side cut. 

This shape is a right rectangular pyramid, which has a base of a rectangle and sides in the shape of triangles; thus, a horizontal cut would make a rectangle. 

A horizontal cut is a side to side cut. 

This shape is rectangular prism, which has a base and sides in the shape of rectangles; thus, the two dimensional shape is a rectangle. 

A horizontal cut is a side to side cut. 

This shape is a right rectangular pyramid, which has a base of a rectangle and sides in the shape of triangles; thus, a horizontal cut would make a rectangle. 

A horizontal cut is a side to side cut. 

This shape is cube, which has a base and sides in the shape of squares; thus, the two dimensional shape is a square. 

The area of a circle can be calculated as , where   is the radius of the circle. 

The circumference can be calculated as , where is the radius of the circle.

The circumference of a circle with radius  inches is 

 inches.

The perimeter of the rectangle is therefore  inches. To find its length, substitute  and  into the equation and solve for :

 inches

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.)  Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 88 inches for our problem. Its total area would be 88 * 88 or 7744 in².

 Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr² or π * 44² = 1936π in². Therefore, the area remaining would be 7744 – 1936π. The cost of the waste would be 0.25 * (7744 – 1936π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 4 from our subtraction. This would give us: 0.25 * 4 * (1936 – 484π). Since 0.25 is equal to 1/4, 0.25 * 4 = 1. Therefore, our final answer is: 1936 – 484π dollars.

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 50 inches for our problem. Its total area would be 50 * 50 or 2500 in².

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr² or π * 25² = 625π in². Therefore, the area remaining would be 2500 - 625π. The cost of the waste would be 0.2 * (2500 – 625π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 5 from our subtraction. This would give us: 0.2 * 5 * (500 – 125π). Since 0.2 is equal to 1/5, 0.2 * 625 = 125. Therefore, our final answer is: 500 – 125π dollars.

In order to solve this problem, we need to recall the formula for the circumference of a circle: 

 or 

The circle in this question provides us with the radius, so we can use the first formula to solve:

Solve:

An isosceles triangle not only has two sides of equal measure, it has two angles of equal measure. This means one of two things, which we examine separately:

Case 1: It has another  angle. This is impossible, since a triangle cannot have two obtuse angles.

Case 2: Its other two angles are the ones that are of equal measure. If we let  be their common measure, then, since the sum of the measures of a triangle is , 

Both angles measure