Question

question 20
which expression gives the volume of a sphere with radius 15?
a. $\frac{4}{3} \pi (15^3)$
b. $4 \pi (15^3)$
c. $\frac{4}{3} \pi (15^2)$
d. $4 \pi (15^2)$

question 21
what is the volume of the sphere shown below?
a. $4000 \pi \text{ units}^3$
b. $\frac{400}{3} \pi \text{ units}^3$
c. $\frac{4000}{3} \pi \text{ units}^3$
d. $400 \pi \text{ units}^3$

question 22
the ratio of the lengths of corresponding parts in two similar solids is 4:1. what is the ratio of their surface areas?
a. 4:1
b. 16:1
c. 8:1
d. 64:1

Explanation:

Question 20

Step1: Recall sphere volume formula

The volume of a sphere is $V=\frac{4}{3}\pi r^3$, where $r$ is radius.

Step2: Substitute $r=15$

Substitute $r=15$ into the formula: $V=\frac{4}{3}\pi (15^3)$

Question 21

Step1: Identify sphere radius

The sphere has diameter 10, so radius $r=\frac{10}{2}=5$.

Step2: Apply volume formula

Substitute $r=5$ into $V=\frac{4}{3}\pi r^3$:
$V=\frac{4}{3}\pi (5^3)=\frac{4}{3}\pi (125)=\frac{4000}{3}\pi$

Question 22

Step1: Recall surface area ratio rule

For similar solids, surface area ratio is the square of the corresponding length ratio.

Step2: Calculate the ratio

Length ratio is $4:1$, so surface area ratio is $4^2:1^2=16:1$

Answer:

Question 20: A. $\frac{4}{3} \pi (15^3)$
Question 21: C. $\frac{4000}{3} \pi$ units$^3$
Question 22: B. 16:1