Question

quiz 11.7.3: spheresquestion 1what is the surface area of the sphere below?a. $324\pi$ units$^2$b. $324\pi^2$ units$^2$c. $36\pi$ units$^2$d. cannot be determinedquestion 2the axis of the sphere below is 12 units in length. what is the surface area of the sphere?a. $256\pi$ units$^2$b. $72\pi$ units$^2$c. $144\pi$ units$^2$d. cannot be determinedquestion 3what is the surface area of a sphere with a radius of 12 units?a. $144\pi$ units$^2$b. $576$ units$^2$c. $576\pi$ units$^2$d. $288\pi$ units$^2$question 4what is the surface area of a sphere with a radius of 11 units?a. $1331\pi$ units$^2$b. $363\pi$ units$^2$c. $726\pi$ units$^2$d. $484\pi$ units$^2$

Explanation:

Question 1

Step1: Identify sphere radius

The sphere has radius $r=9$.

Step2: Apply surface area formula

Surface area of a sphere: $SA=4\pi r^2$
Substitute $r=9$:
$SA=4\pi (9)^2 = 4\pi \times 81 = 324\pi$

Question 2

Step1: Find radius from axis length

The axis (diameter) is 12, so $r=\frac{12}{2}=6$.

Step2: Calculate surface area

Use $SA=4\pi r^2$:
$SA=4\pi (6)^2 = 4\pi \times 36 = 144\pi$

Question 3

Step1: Use given radius $r=12$

Step2: Compute surface area

$SA=4\pi r^2 = 4\pi (12)^2 = 4\pi \times 144 = 576\pi$

Question 4

Step1: Use given radius $r=11$

Step2: Compute surface area

$SA=4\pi r^2 = 4\pi (11)^2 = 4\pi \times 121 = 484\pi$

Answer:

1. A. $324\pi$ units$^2$
2. C. $144\pi$ units$^2$
3. C. $576\pi$ units$^2$
4. D. $484\pi$ units$^2$