This worksheet has 20 problems on circles, aligned with Common Core standard 7.G.B.4. The first problems practice radius, diameter, circumference, and area of a single circle. Each problem says whether to use \(3.14\) for \(\pi\) or to leave the answer in terms of \(\pi\).
The last problems are word problems with a bicycle wheel, lace trim, a sprinkler, a window, a gravel path, and a flower bed. Label every answer with the correct unit, using square units for area.
Problem 1: Radius and diameter
The circle shows a diameter of \(14\text{ cm}\). Find its radius. Then find the diameter of a circle with radius \(9\text{ in}\).
Problem 2: Diameter and radius pairs
Find the missing measure of each circle.
- The diameter is \(22\text{ cm}\). Find the radius.
- The radius is \(15\text{ in}\). Find the diameter.
- The diameter is \(3.5\text{ ft}\). Find the radius.
Problem 3: Circumference from the diameter
Find the circumference of the circle. Use \(3.14\) for \(\pi\).
Problem 4: Labeled diameter
Find the circumference of the circle. Use \(3.14\) for \(\pi\).
Problem 5: Circumference from the radius
Find the circumference of the circle. Use \(3.14\) for \(\pi\).
Problem 6: Fence around a garden
A circular garden has a radius of \(12\text{ m}\). Find the length of fence needed to go all the way around it. Use \(3.14\) for \(\pi\).
Problem 7: Area from the radius
Find the area of the circle. Use \(3.14\) for \(\pi\).
Problem 8: Labeled radius
Find the area of the circle. Use \(3.14\) for \(\pi\).
Problem 9: Area from the diameter
A circular rug has a diameter of \(20\text{ cm}\) on a model. Find its area. Use \(3.14\) for \(\pi\).
Problem 10: Circular patio
A circular patio has a diameter of \(16\text{ ft}\). Find its area. Use \(3.14\) for \(\pi\).
Problem 11: Answers in terms of pi
A circle has radius \(8\text{ cm}\). Find its circumference and its area. Leave both answers in terms of \(\pi\).
Problem 12: Exact answers with pi
A circle has radius \(11\text{ m}\). Find its circumference and its area. Leave both answers in terms of \(\pi\).
Problem 13: Work backward from circumference
A circle has a circumference of \(62.8\text{ cm}\). Find its diameter and its radius. Use \(3.14\) for \(\pi\).
Problem 14: Work backward from area
A circle has an area of \(706.5\text{ cm}^{2}\). Find its radius, its diameter, and its circumference. Use \(3.14\) for \(\pi\).
Problem 15: Bicycle wheel
Maya’s bicycle wheel has a diameter of \(26\text{ in}\). How far does the bike roll in \(10\) full turns of the wheel? Use \(3.14\) for \(\pi\).
Problem 16: Lace trim
Mei sews lace trim around the edge of a round tablecloth with a radius of \(36\text{ in}\). Lace costs $1.50 per foot and can be cut to any length. Find the length of lace in inches and in feet, and then the cost. Use \(3.14\) for \(\pi\).
Problem 17: Sprinkler coverage
Liam’s lawn is a square \(24\text{ ft}\) on each side. A sprinkler in the center waters a circle with a radius of \(12\text{ ft}\). Find the area of the lawn that does not get watered. Use \(3.14\) for \(\pi\).
Problem 18: Window with a semicircle
A window is a rectangle \(6\text{ ft}\) wide and \(4\text{ ft}\) tall with a semicircle on top. Find the total area of glass. Use \(3.14\) for \(\pi\).
Problem 19: Gravel path
A circular pond has a radius of \(6\text{ ft}\). A gravel path \(2\text{ ft}\) wide goes all the way around the pond. Find the area of the path. Use \(3.14\) for \(\pi\).
Problem 20: Quarter-circle flower bed
Jamal’s flower bed is a quarter circle with both straight edges \(10\text{ ft}\) long. (a) Find the area of the bed. (b) Find the length of fence needed to go all the way around it. Use \(3.14\) for \(\pi\).
See every chapter on the Grade 7 math page.