Question

1. which of the following units is appropriate for measuring the volume of a sphere?

a. meters
b. square centimeters
c. cubic centimeters
d. centimeters

1. what happens to the volume of a sphere if the radius is tripled?

a. the volume is tripled.
b. the volume decreases.
c. the volume is doubled.
d. the volume increases by 27 times.

1. what is the distance from the center of a sphere to any point on its surface called?

a. circumference
b. diameter
c. volume
d. radius

1. what is the term for the distance across a sphere through its center?

a. diameter
b. circumference
c. volume
d. radius

1. what is the volume of a sphere with a radius of 3 cm?

a. 36π cm³
b. 56 cm³
c. 27 cm³
d. other cm³

Explanation:

Step1: Solve Q1 (Volume unit)

Volume uses 3D units; cubic centimeters fit.

Step2: Solve Q2 (Volume scaling)

Sphere volume: $V=\frac{4}{3}\pi r^3$. New $r'=3r$, so $V'=\frac{4}{3}\pi (3r)^3=27\times\frac{4}{3}\pi r^3=27V$.

Step3: Solve Q3 (Center to surface term)

By definition, this distance is radius.

Step4: Solve Q4 (Through-center distance)

By definition, this distance is diameter.

Step5: Solve Q5 (Volume calculation)

Substitute $r=3$ into $V=\frac{4}{3}\pi r^3$: $V=\frac{4}{3}\pi (3)^3=36\pi$.

Answer:

1. c. Cubic centimeters
2. d. The volume increases by 27 times
3. d. Radius
4. a. Diameter
5. b. $36\ \text{cm}^3$