Question

Twice Use what you have learned to compare circles by their characteristics. 1. Draw each circle. A. Radius length of 3 centimeters b. Diameter length of 3 centimeters 2. Describe the similarities and differences between your two circles. 3. Describe the relationship between the circumferences of the two circles. 4. Describe the circumference-to-diameter ratio of all circles.

Answer 1

Answer:

1. a. Please find attached, the diagram for the first circle with radius = 3 cm

b. Please find attached, the diagram for the second circle with diameter = 3 cm

2. The similarities are;

a) Both circles can be described by a point and a radius or a diameter

The differences are;

a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)

b) The circumferences of the two circles are different

c) The area covered by the two circles are different

3. The circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm

4. The circumference to diameter ratio of the circle with radius  = 3 cm is π

The circumference to diameter ratio of the circle with diameter  = 3 cm is π

Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter

Step-by-step explanation:

1. a. The radius length of the first circle = 3 cm

The diagram for the first circle with radius 3 cm is attached

b. The diameter length of the second circle = 3 cm

The diagram for the second circle with diameter 3 cm is attached

2. The similarities are;

a) Both circles can be described by a point and a radius or a diameter

The differences are;

a) The length of the radiuses are different for the two circles (3 cm and 1.5 cm)

b) The circumferences of the two circles are different

c) The area covered by the two circles are different

3. The circumference of the circle with radius equal to 3 cm is 2 × π × 3 = 6·π cm

The circumference of the circle with diameter equal to 3 cm is π × 3 = 3·π cm

Therefore, the circumference of the circle with radius equal to 3 cm is larger than the circumference of the circle with diameter equal to 3 cm

4. The circumference to diameter ratio of the circle with radius = 3 cm is 6·π cm/(2 × 3 cm) = π

The circumference to diameter ratio of the circle with diameter = 3 cm is 3·π cm/(3 cm) = π.

Both circles have equal circumference to diameter ratio given that the circumference = π × The diameter.