Mathematics
Grade 8
15 min
Circles: word problems
Circles: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify the radius and diameter of a circle from given word problems.
Select the correct formula (circumference or area) to solve a given word problem involving circles.
Calculate the circumference of a circle given its radius or diameter, and interpret the result in context.
Calculate the area of a circle given its radius or diameter, and interpret the result in context.
Solve multi-step word problems that require finding unknown dimensions of a circle.
Apply appropriate units to their answers for circumference and area problems.
Use the value of $\pi$ (either as a symbol or an approximation) correctly in calculations.
Ever wondered how much ribbon you'd need to go around a giant birthday cake, or how much grass seed to buy for a circular lawn?...
2
Key Concepts & Vocabulary
TermDefinitionExample
CircleA set of all points in a plane that are equidistant from a fixed point called the center.A hula hoop or the face of a clock are examples of circles.
Radius (r)The distance from the center of a circle to any point on its edge.If you draw a line from the center of a pizza to its crust, that's the radius.
Diameter (d)The distance across a circle passing through its center. It's twice the radius.The length of a straight cut across a pizza that goes through its middle is the diameter.
Circumference (C)The distance around the outside of a circle. It's like the perimeter of a polygon.The length of the crust all the way around a pizza is its circumference.
Area (A)The amount of surface enclosed within a circle.The amount of cheese and toppings on a pizza...
3
Core Formulas
Circumference of a Circle
$C = \pi d$ or $C = 2\pi r$
Use this formula when you need to find the distance around a circle. 'd' is the diameter, and 'r' is the radius. Remember, $d = 2r$.
Area of a Circle
$A = \pi r^2$
Use this formula when you need to find the amount of space or surface inside a circle. 'r' is the radius, and $r^2$ means $r \times r$.
Relationship between Diameter and Radius
$d = 2r$ or $r = \frac{d}{2}$
This rule helps you convert between diameter and radius, which is often necessary to use the correct formula.
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Challenging
A circular table with a diameter of 4 feet is placed in the center of a square room with side lengths of 6 feet. What is the area of the floor space that is NOT covered by the table? Use π ≈ 3.14.
A.23.44 sq ft
B.27.84 sq ft
C.31.44 sq ft
D.36.00 sq ft
Challenging
A square is inscribed in a circle. The diagonal of the square is 10 cm long and is also the diameter of the circle. What is the area of the circle? (Leave your answer in terms of π).
A.10π cm²
B.50π cm²
C.100π cm²
D.25π cm²
Challenging
A race car travels along a circular track. After completing exactly one-quarter of a lap, it has traveled 157 meters. What is the approximate area of the land enclosed by the track? Use π ≈ 3.14.
A.31,400 m²
B.7,850 m²
C.10,000 m²
D.200 m²
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