Question

1. the volume of a cylinder is directly proportional to which of the following?

a. diameter only
b. base area and height
c. height only
d. radius only

1. a pizza has a radius of 6 cm. what is its area?

a. 36π cm²
b. 14π cm²
c. 36π cm²
d. 72π cm²

1. find the diameter of a circle with an area of 78.5 square meters. use π ≈ 3.14.

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

1. according to cavalieri’s principle, when comparing two solids of equal height and cross - sectional areas, what can be concluded about their volumes?

a. the solid with the smaller base area has a greater volume
b. their volumes are different
c. the solid with the larger surface area has a greater volume
d. their volumes are equal

1. a pizza has a diameter of 16 inches. what is its circumference?

a. 25.12 inches
b. 50.24 inches
c. 40 inches
d. 32 inches

1. a circular table has a radius of 5 meters. calculate the diameter.

a. 5 meters
b. 15 meters
c. 10 meters
d. 2.5 meters

1. if the area of a circle is 78.5 square meters, what is the radius?

Explanation:

Step1: Solve Q8 (Cylinder Volume Proportion)

Recall cylinder volume formula: $V = \pi r^2 h$, where $\pi r^2$ is base area. Volume is directly proportional to base area and height.

Step2: Solve Q9 (Circle Area)

Use circle area formula $A = \pi r^2$. Substitute $r=6$: $A = \pi (6)^2 = 36\pi$ $\text{cm}^2$.

Step3: Solve Q10 (Circle Diameter from Area)

Rearrange area formula: $r = \sqrt{\frac{A}{\pi}}$. Substitute $A=78.5, \pi=3.14$: $r = \sqrt{\frac{78.5}{3.14}} = \sqrt{25} = 5$ m. Diameter $d=2r=10$ m.

Step4: Solve Q11 (Cavalieri's Principle)

Cavalieri's Principle states solids with equal height and equal cross-sectional areas at every level have equal volumes.

Step5: Solve Q12 (Circle Circumference)

Use circumference formula $C = \pi d$. Substitute $d=16, \pi=3.14$: $C = 3.14 \times 16 = 50.24$ inches.

Step6: Solve Q13 (Circle Diameter from Radius)

Diameter formula: $d=2r$. Substitute $r=5$: $d=2 \times 5 = 10$ meters.

Step7: Solve Q14 (Circle Radius from Area)

Rearrange area formula: $r = \sqrt{\frac{A}{\pi}}$. Substitute $A=78.5, \pi=3.14$: $r = \sqrt{\frac{78.5}{3.14}} = \sqrt{25} = 5$ meters.

Answer:

1. b. Base area and height
2. a. $36\pi$ $\text{cm}^2$
3. c. 10 meters
4. d. Their volumes are equal
5. b. 50.24 inches
6. c. 10 meters
7. c. 5 meters