Question

1 what is the circumference of a circle with a diameter of 14 meters?
a. 43.96 meters
b. 2198 meters
c. 56 meters
d. 28 meters

1. a circular table top has an area of 706.5 square meters. what is its radius?

a. 10 meters
b. 15 meters
c. 5 meters
d. 20 meters

1. if the circumference of a circle is 50 meters, what is its diameter?

a. 25 meters
b. 17 meters
c. 15.92 meters
d. 10.72 meters

1. what does the term cross - sectional area refer to in the context of cavalieri’s principle?

a. the area of a two - dimensional slice of a solid at a given height
b. the length of the base of a solid
c. the volume of a solid at a specific height
d. the total surface area of a solid

1. how do you find the diameter of a circle if you know its circumference?

a. multiply the circumference by π
b. divide the radius by π
c. circumference divided by π
d. multiply the radius by 2π

1. if a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

a. 75π cm³
b. 75 cm³
c. 45π cm³
d. 45 cm³

1. a circular track has a diameter of 100 meters. what is the circumference? use π ≈ 3.14

a. 150 meters
b. 200 meters
c. 314 meters
d. 250 meters

Explanation:

Step1: Calculate circle circumference

$C = \pi d = 3.14 \times 14 = 43.96$ meters

Step2: Solve for circle radius

$A = \pi r^2 \implies r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{78.5}{3.14}} = 5$ meters

Step3: Find diameter from circumference

$d = \frac{C}{\pi} = \frac{50}{3.14} \approx 15.92$ meters

Step4: Define cross-sectional area

Identify the correct definition from Cavalieri's Principle.

Step5: Relate circumference and diameter

Recall the formula rearranged for diameter.

Step6: Calculate cylinder volume

$V = \pi r^2 h = \pi \times 3^2 \times 5 = 45\pi$ cm³

Step7: Calculate track circumference

$C = \pi d = 3.14 \times 100 = 314$ meters

Answer:

1. a. 43.96 meters
2. c. 5 meters
3. c. 15.92 meters
4. a. The area of a two-dimensional slice of a solid at a given height
5. c. Circumference divided by $\pi$
6. d. $45\pi$ cm³
7. c. 314 meters