Grade 7 | Unit 3 | Lesson 7: Exploring the Area of a Circle | Practice Problems

The x-axis of each graph has the diameter of a circle in meters. Label the y-axis on each graph with the appropriate measurement of a circle: radius (m), circumference (m), or area (m2). Description: Three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's. First graph is curved upward from left to right, begins at the origin, passes through 2 comma 3, 3 comma 7, 4 comma 12, 5 comma 19. Second graph is an upward line from left to right, begins at the origin, passes through 2 comma 1, 4 comma 2, 6 comma 3, 8 comma 4. Third graph is an upward line from left to right, begins at the origin, passes through 2 comma approximately 6 and 28 hundredths, 4 comma approximately 12 and 56 hundredths, 6 comma 18 and 84 hundredths.

• The first graph shows the relationship between the diameter and area of a circle.

• The second graph shows the relationship between the diameter and the radius.

• The third graph shows the relationship between the diameter and the circumference.

Tags

CCSS.7.G.B.4

Circle A has area 500 in2. The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.

Lin’s bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels?

Tags

CCSS.HSG.GPE.A.1

Priya drew a circle whose circumference is 25 cm. Clare drew a circle whose diameter is 3 times the diameter of Priya’s circle. What is the circumference of Clare’s circle?

Tags

CCSS.7.G.B.4

Here is a picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 2 square units but less than 4 square units. Description: Two squares and circle on a grid of 4 units by 4 units. In the center of the grid is a square that measures two units high by two units wide. Within the square is a circle, with a diameter of 2 units. Within the circle is another square, rotated so that the each of the four vertices of the square meet with a point of the circle and the midpoint of the larger square.

Here is another picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 18 square units and less than 36 square units. Description: A square with a circle inside of it and a square inside of the circle. The shapes are drawn on a grid. The outer square has side lengths = 6 units. The Circle has diameter = 6 units. The inner square is turned such that its four corners correspond with the midpoints of each side of the outer square.

Point A is the center of the circle, and the length of CD is 15 centimeters. Find the circumference of this circle.

Tags

CCSS.HSG.C.B.5