Area of a Circle: Why Quadratic?
Read this topicExplanations 5
- Suppose that you have a circle of radius RRR, and you would like to find its area. We will use an intuitive formula that can be proved later using calculus. Consider a circle wi…
By Sujay Kazi
- Suppose that you have a circle of radius r.r.r. Inside this circle, inscribe a regular polygon with nnn sides; we will use this polygon to approximate the area of the circle. Th…
By Sujay Kazi
- (Videos) Area of a Circle by Art of Problem Solving Here's a set of amazing videos on circular areas from Art of Problem Solving. The first illustrates a more intuitive basis fo…
By Liza Sulkin, Alex Federspiel
- Here's a great video that provides some intuition behind the circle area formula!
By Liza Sulkin
- Here's an awesome video that goes through some unusual problems involving circular areas.
By Liza Sulkin
Problems 21
- What is the area of a circle with radius 5 cm?
- What is the power converted from the wind?
- What is the area of the white shape?
- You have traveled west on the Oregon Trail, survived dysentery, and have staked your claim on a new plot of land. You have 4 miles of fence which you can put in any shape you'd …
- Expii's engineers are working late into the night and are ordering pizza. Carl's Pizza has a medium 16-inch pizza or a large 18-inch pizza. How much more pizza is in the 18-inch…
- What is the area of the above pizza?
- The diameter of the above (world-class, apparently) frisbee is 101010 inches. What is the area of its face?
- A large pizza costs 20. If the pizza is 16 inches across, what is the price of the pizza per square inch (rounded to the nearest cent)?
- You've been given a bag of chocolate coins! As you start to unwrap them, you notice that the diameter of the circular wrapper is actually 4 mm longer than that of the coin itsel…
- One night, you decide to order some pizza for dinner. The nearest pizza shop offers the following deals: (1) A 12-inch pizza for \10. (2) A 17-inch pizza for \20. Assuming you p…
- The Macy’s Day Parade is trying out a new route for this year’s Thanksgiving celebration. You’re the head of planning, and can direct the 4 miles of parade to march in any shape…
- What is the area of a circle with radius 8z8z8z?
- What is the area of a circle with radius 1x\frac{1}{x}x1?
- What is the area of a circle with diameter 10π10\pi10π?
- What is the area of a circle with diameter 4y\frac{4}{y}y4?
- Suppose you have a circle where the magnitude of the radius (i.e. the value without the units) is equal to the magnitude of the area. What is the radius?
- What is the area of a circle with circumference 6π6\pi6π?
- What is the area of a circle with circumference 9π\frac{9}{\pi}π9?
- What is the radius of a circle with area 169π169\pi169π?
- What is the diameter of a circle with area π4\frac{\pi}{4}4π?
- What is the circumference of a circle of area 49π49\pi49π?