A rectangle has sides 18 cm by 14 cm. What is the area of the largest circle that can be drawn completely inside this rectangle (in square centimetres, sq cm)?

Introduction:
This question tests the concept of fitting the largest possible circle inside a rectangle. A circle drawn inside a rectangle must have its diameter no larger than the rectangle’s smaller side, otherwise it would extend outside. Therefore, the largest inscribed circle inside a rectangle is limited by the rectangle’s minimum side. Once we identify the diameter, we compute the radius and then use the circle area formula. The numbers here are chosen so that using pi = 22/7 gives a clean integer answer.

Given Data / Assumptions:

• Rectangle sides = 18 cm and 14 cm• Largest inscribed circle diameter = smaller side of rectangle• Use pi = 22/7 for area calculation

Concept / Approach:
The maximum diameter of the circle is limited by the smaller dimension of the rectangle. So diameter = 14 cm, radius = 7 cm. Area = pi*r^2 = pi*49. Substitute pi = 22/7 to get 154 sq cm.

Step-by-Step Solution:
Step 1: Identify the limiting side.Smaller side = 14 cmStep 2: Set circle diameter equal to the smaller side.Diameter = 14 cmRadius r = 14/2 = 7 cmStep 3: Compute circle area.Area = pi * r^2 = pi * 7^2 = 49*piStep 4: Substitute pi = 22/7.Area = 49*(22/7) = 7*22 = 154 sq cm

Verification / Alternative check:
A circle of diameter 14 cm fits within the 14 cm side exactly and will also fit within the 18 cm side because 14 < 18. Any circle larger than 14 cm diameter would exceed the 14 cm width and would not fit. Therefore this is truly the largest possible. The computed area 154 is consistent with radius 7 and pi = 22/7.

Why Other Options Are Wrong:
49 is just r^2 and ignores multiplication by pi.378 and 308 correspond to larger radii that would require diameter greater than 14 cm, which cannot fit.1078 is far too large and not feasible for a circle inside this rectangle.

Common Pitfalls:
• Using the longer side (18 cm) as diameter instead of the shorter side.• Forgetting to halve the diameter to get the radius.• Forgetting pi in the area formula or using an inconsistent pi value mid-calculation.

Final Answer:
The area of the largest circle is 154 sq cm.