Question

The width of the smaller rectangular box is 6.25 inches. The width of a similar larger rectangular box is 8.75 inches. Estimate the length of the larger rectangular box.

Answer 1

To estimate the length of the larger rectangular box, use the concept of similarity and set up a proportion using the widths of the two boxes. Use the scale factor to find the length of the larger box.

Step-by-step explanation:

To estimate the length of the larger rectangular box, we can use the concept of similarity. The problem states that the width of the smaller box is 6.25 inches and the width of the larger box is 8.75 inches. Since the boxes are similar, we can set up a proportion to find the scale factor:

Scale factor = width of larger box / width of smaller box

Scale factor = 8.75 inches / 6.25 inches

Now, we can use the scale factor to find the length of the larger box:

Length of larger box = scale factor x length of smaller box

Length of larger box = scale factor x width of larger box = 8.75 inches x (length of smaller box / width of smaller box)

Answer 2

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this formula, π (pi) is a mathematical constant approximately equal to 3.14159. To find the circumference, you simply multiply 2π by the radius. This formula is derived from the definition of pi, which is the ratio of the circumference of any circle to its diameter.

For a more concrete example, let's consider a circle with a radius (r) of 5 units. Using the formula C = 2πr, we can substitute the value of r to find the circumference. C = 2π 5 = 10π units. If you want a numerical approximation, it's approximately 31.4159 units. This means that if you were to measure around the circle, it would be approximately 31.4159 units in length.

Understanding the relationship between the circumference and radius is fundamental in geometry and real-world applications. Whether you're dealing with circles in mathematics, physics, or engineering, knowing how to calculate the circumference provides valuable insights into the size and dimensions of circular objects. This formula is a cornerstone in geometry, enabling us to quantify the measurement of circles and their components.