Testinar Grade 7 math

Circumference of a Circle

Students will build Grade 7 mastery of circumference of a circle using models, equations, and test-style reasoning.

CH07-02 Measurement Geometry

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A circle has a radius of \(5\) meters. Approximately, what is its circumference? Use \(\pi\approx3.14\).
1. \(15.7\) m
2. \(25\) m
3. \(31.4\) m
4. \(78.5\) m
A circle has a diameter of \(12\) cm. What is the circumference? Use \(\pi\approx\frac{22}{7}\).
1. \(\frac{264}{7}\) cm
2. \(\frac{132}{7}\) cm
3. \(\frac{528}{7}\) cm
4. \(113\) cm
If a circle's radius is \(7\) inches, which expression gives its circumference?
1. \(7\pi\)
2. \(14\pi\)
3. \(49\pi\)
4. \(28\pi\)
A circle has diameter \(20\) ft. What is its circumference to the nearest tenth? Use \(\pi\approx3.14\).
1. \(31.4\) ft
2. \(62.8\) ft
3. \(125.6\) ft
4. \(314\) ft
A wheel has radius \(0.5\) m. If it rotates exactly once, how far does it travel? Use \(\pi\approx3.14\).
1. \(0.78\) m
2. \(1.57\) m
3. \(3.14\) m
4. \(6.28\) m
A circular pond has circumference \(44\) meters. Using \(\pi\approx\frac{22}{7}\), what is its diameter?
1. \(7\) m
2. \(14\) m
3. \(22\) m
4. \(44\) m
Which circle below has a circumference of approximately \(37.7\) cm? Use \(\pi\approx3.14\).
1. Radius \(6\) cm
2. Diameter \(6\) cm
3. Radius \(6\) cm, but using \(C=\pi r\) (incorrect formula)
4. Diameter \(12\) cm
If a circle has circumference \(100\) cm, what is its radius? (Use \(\pi\approx3.14\), round to nearest whole.)
1. About \(16\) cm
2. About \(32\) cm
3. About \(50\) cm
4. About \(64\) cm

Teacher and parent reference

Answer key and explanations

C. \(31.4\) m
Circumference \(=2\pi r\approx2\times3.14\times5=31.4\) m.
A. \(\frac{264}{7}\) cm
\(C=\pi d=\frac{22}{7}\times12=\frac{264}{7}\approx37.7\) cm.
B. \(14\pi\)
\(C=2\pi r=2\pi(7)=14\pi\) in.
B. \(62.8\) ft
\(C=\pi d=3.14\times20=62.8\) ft.
C. \(3.14\) m
Distance = circumference = \(2\pi r=2\times3.14\times0.5=3.14\) m.
B. \(14\) m
\(C=\pi d \Rightarrow 44=\frac{22}{7}d \Rightarrow d=44\div\frac{22}{7}=44\times\frac{7}{22}=14\) m.
A. Radius \(6\) cm
\(C=2\pi r=2\times3.14\times6=37.68\approx37.7\) cm (A); B: \(C=\pi d=3.14\times6=18.84\) cm (wrong); C: confuses formula; D: \(C=\pi d=3.14\times12=37.68\) cm (close, but uses diameter not radius).
A. About \(16\) cm
\(C=2\pi r \Rightarrow 100=2\times3.14\times r \Rightarrow r=100\div6.28\approx16\) cm.