Radius — Grade 7 Math, what it means and where it is taught
Centre to edge. Half the diameter.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Standard form — (x-h)2 + (y-k)2 = r2, centre (h,k) and radius r.
- Radian — The angle whose arc length equals the radius. A full turn is 2π radians.
- Unit circle — The circle of radius 1 centred at the origin.
Practise this idea
57 questions in the course bank use Radius, in Length and Area in 2-D Figures, Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Circles, Volume of Cylinders, Cones & Spheres, Circle Angles, Arcs & Chords. The first 8 are below; the rest are in those units.
Problem 1
Find the circumference of a circle with radius 3. Use π ≈ 3.14.
Worked answer
18.84
2 × 3.14 × 3 = 18.84
Problem 2
Find the area of a circle with radius 5. Use π ≈ 3.14.
Worked answer
78.5
52 = 25
3.14 × 25 = 78.5
Problem 3
Find the area of a circle with diameter 14. Use π ≈ 227.
Worked answer
154
r = 7
227 × 49 = 22 × 7 = 154
Problem 4
A square of side 10 cm has a circle of diameter 10 cm cut out. Find the remaining area. Use π ≈ 3.14.
Worked answer
21.5
Square: 100 cm2
Circle: 3.14 × 25 = 78.5 cm2
100 - 78.5 = 21.5 cm2
Problem 5
A circle has circumference 31.4. Find its radius. Use π ≈ 3.14.
Worked answer
5
31.4 = 6.28r
r = 31.4 ÷ 6.28 = 5
Problem 6
A shape is a 10 × 6 rectangle with a semicircle of diameter 6 on one end. Find its total area. Use π ≈ 3.14.
Worked answer
74.13
Rectangle: 10 × 6 = 60
Semicircle: 12 × 3.14 × 32 = 14.13
60 + 14.13 = 74.13
Problem 7
A circular path has outer radius 10 and inner radius 7. Find the area of the ring. Use π ≈ 3.14.
Worked answer
160.14
Outer: 3.14 × 100 = 314
Inner: 3.14 × 49 = 153.86
314 - 153.86 = 160.14
Note π(102 - 72) = 51π, not π(3)2.
Problem 8
A cylinder has radius 4 cm and height 10 cm. It is cut vertically through its axis. Find the area of the cross section.
Worked answer
80
Height = 10 cm
Width = 2 × 4 = 8 cm
Area = 10 × 8 = 80 cm2