The Length of a Rectangle and Its Relation to the Diameter of a Circle

In geometry, understanding the relationships between different shapes can provide insights into calculating areas and other measurements. Consider a situation where we know the length of a rectangle and it is related to the diameter of a circle. This article will explore the problem of finding the area of a circle given that the length of a rectangle is 16 cm and this length is more than the diameter of a circle by 4 cm. Let's break it down step by step.

ID 1: Detailed Solution and Calculation

Given that the length of the rectangle is 16 cm, which is more than the diameter of a circle by 4 cm:

Diameter of the circle 18 - 4 14 cm

Radius of the circle 14 / 2 7 cm

Area of the circle πr2 (22/7) × 7 2 154 sq cm

ID 2: Alternative Approach to Calculate the Radius and Area of the Circle

Another approach to solving the same problem is as follows:

If the length of the rectangle is 18 cm and it is 4 cm more than the diameter of the circle, we can find the diameter:

Diameter of the circle 18 - 4 14 cm

To find the radius, we divide the diameter by 2:

Radius of the circle 14 / 2 7 cm

Now, using the formula for the area of a circle, we get:

Area of the circle πr2 (22/7) × 7 2 154 cm2

ID 3: Analyzing with a Chord and Pythagoras' Theorem

Another interesting approach involves using the chord of the rectangle to solve for the radius and area of the circle:

If we connect a chord, which is the length of the rectangle, to the center of the circle, we create a right-angled triangle with the radius as one of its sides. Using this setup, we can derive the radius squared:

2r2 16

r2 8

Area A πr2 8π cm2

ID 4: Inscribed Circle Scenario

While the problem statement is not entirely clear, if we assume the circle is inscribed within the rectangle, we can solve it differently:

If the length of the rectangle is 24 cm and the diameter of the circle is 14 cm (10 cm is subtracted from the length), we can infer:

The width of the rectangle 14 cm

Therefore, the area of the rectangle 24 × 14 336 sq cm

These examples highlight the importance of understanding the relationships between shapes and the application of mathematical principles to solve geometric problems.