Question

question 5
the area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units.
a. true
b. false

question 6
what is the volume of the sphere below?
a. $27\pi$ units$^3$
b. $12\pi$ units$^3$
c. $36\pi$ units$^3$
d. $81\pi$ units$^3$

question 7
what is the volume of a sphere with a radius of 6 units?
a. $864\pi$ units$^3$
b. $288\pi$ units$^3$
c. $216\pi$ units$^3$
d. $144\pi$ units$^3$

question 8
what is the volume of a sphere with a radius of 18 units?
a. $7776\pi$ units$^3$
b. $1296\pi$ units$^3$
c. $5832\pi$ units$^3$
d. $1944\pi$ units$^3$

question 9
given a sphere with radius $r$, the formula $4\pi r^2$ gives ______.
a. the volume
b. the surface area
c. the radius
d. the cross-sectional area

Explanation:

Question 5

Step1: Calculate circle area

$A_{circle} = \pi r^2 = \pi (12)^2 = 144\pi$

Step2: Calculate sphere surface area

$A_{sphere} = 4\pi r^2 = 4\pi (6)^2 = 144\pi$

Step3: Compare the two values

$144\pi = 144\pi$, so the statement is true.

Question 6

Step1: Recall sphere volume formula

$V = \frac{4}{3}\pi r^3$

Step2: Substitute $r=3$

$V = \frac{4}{3}\pi (3)^3 = \frac{4}{3}\pi \times 27 = 36\pi$

Question 7

Step1: Recall sphere volume formula

$V = \frac{4}{3}\pi r^3$

Step2: Substitute $r=6$

$V = \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi \times 216 = 288\pi$

Question 8

Step1: Recall sphere volume formula

$V = \frac{4}{3}\pi r^3$

Step2: Substitute $r=18$

$V = \frac{4}{3}\pi (18)^3 = \frac{4}{3}\pi \times 5832 = 7776\pi$

Question 9

Step1: Match formula to sphere property

The formula $4\pi r^2$ is defined as the surface area of a sphere.

Answer:

Question 5: A. True
Question 6: C. $36\pi$ units$^3$
Question 7: B. $288\pi$ units$^3$
Question 8: A. $7776\pi$ units$^3$
Question 9: B. the surface area