Question

question 4
the two solids below are similar, and the ratio between the lengths of their edges is 4:5. what is the ratio of their surface areas?
a. 16:25
b. 64:125
c. 16:20
d. 5:4

question 5
if the ratio between the radii of the two spheres is 3:5, what is the ratio of their volumes?
a. 3:25
b. 6:25
c. 27:125
d. 9:25

question 6
if two pyramids are similar and the ratio between the lengths of their edges is 4:9, what is the ratio of their volumes?
a. 64:729
b. 16:81
c. 4:9
d. 81:16

Explanation:

Question 4

Step1: Recall surface area ratio rule

For similar solids, the ratio of surface areas is the square of the ratio of corresponding linear measurements.

Step2: Calculate the squared ratio

Edge length ratio = $4:5$, so surface area ratio = $4^2:5^2 = 16:25$

Question 5

Step1: Recall volume ratio rule

For similar solids, the ratio of volumes is the cube of the ratio of corresponding linear measurements.

Step2: Calculate the cubed ratio

Radius ratio = $3:5$, so volume ratio = $3^3:5^3 = 27:125$

Question 6

Step1: Recall volume ratio rule

For similar solids, the ratio of volumes is the cube of the ratio of corresponding linear measurements.

Step2: Calculate the cubed ratio

Edge length ratio = $4:9$, so volume ratio = $4^3:9^3 = 64:729$

Answer:

Question 4: A. 16:25
Question 5: C. 27:125
Question 6: A. 64:729