The area of a circle can be calculated by_____.

The area of a circle can be calculated by_____.

• A. Pi* r^2
• B. Pi*(D^2/4)
• C. 0.7854*D^2
• D. All of the above

Answer: (D)

The area of a circle relates to the square of its size. Start with A = πr^2. If you express everything in terms of diameter, r = D/2, so A = π(D/2)^2 = πD^2/4. That shows the second form is just a rewrite of the first using diameter. The decimal 0.7854 is an approximation of π/4, so multiplying D^2 by 0.7854 gives a close, practical estimate of the same area. Because all three expressions yield the same value (with the decimal form being an approximation), all of these are valid ways to calculate the circle’s area.

The area of a circle relates to the square of its size. Start with A = πr^2. If you express everything in terms of diameter, r = D/2, so A = π(D/2)^2 = πD^2/4. That shows the second form is just a rewrite of the first using diameter. The decimal 0.7854 is an approximation of π/4, so multiplying D^2 by 0.7854 gives a close, practical estimate of the same area. Because all three expressions yield the same value (with the decimal form being an approximation), all of these are valid ways to calculate the circle’s area.