Area & Circumference of Circles Flashcards

All 8 cards in this deck

What is the formula for the circumference of a circle?

$C = 2\pi r = \pi d$

What is the formula for the area of a circle?

$A = \pi r^2$

True or false? For a circle of diameter $10$ cm, the area is $\pi \times 10^2$.

False. You must halve the diameter first: area $= \pi \times 5^2$.

What are the steps to find the radius of a circle from its circumference?

e.g. circumference $= 12\pi$ cm

1. Divide the circumference by $\pi$ to get the diameter: $12\pi \div \pi = 12$ cm

2. Halve the diameter: $r = 6$ cm

What are the steps to find the perimeter of a semicircle?

e.g. radius $4$ cm

1. Half the circumference: $\frac{1}{2} \times 2\pi \times 4 = 4\pi$ cm

2. Add the diameter (the straight edge): $4\pi + 8$ cm

What are the steps to work out how many boxes of seed are needed to cover a circular lawn?

e.g. lawn of radius $10$ m, one box covers $50$ m$^2$

1. Area of circle: $\pi \times 10^2 = 314.1...$ m$^2$

2. Divide by the coverage: $314.1... \div 50 = 6.28...$

3. Round up to a whole box: $7$ boxes

What are the steps to find the area of a shape made from a rectangle with a semicircle on one end?
e.g. rectangle $10$ cm by $6$ cm, with a semicircle of diameter $6$ cm on one end

1. Area of the rectangle: $10 \times 6 = 60$ cm$^2$
2. Area of the semicircle: $\frac{1}{2} \times \pi \times 3^2 = 14.13...$ cm$^2$
3. Add the parts: total area $= 74.1$ cm$^2$ (3 s.f.)

True or false? To find the perimeter of a shape made from a rectangle with a semicircle joined to one end, you include the straight edge where the two shapes meet.

False. That edge is inside the shape, so the perimeter is the three outer sides of the rectangle plus the semicircle's arc.