Surface Area of a Cuboid and Cube MCQs

Q1. Two cubes have their edges in the ratio 2:3. Working from edge to face to whole, the ratio of their total surface areas is?

• A.4:9
• B.2:3
• C.8:27
• D.4:6

Answer: A. 4:9

Quick parse - a typical math numerical. The data on the table: 2, 3. We are after the quantity the stem asks for. Tool of choice - edge ratio = 2:3. Rearrange it for the unknown before substituting. Numbers in: edge ratio = 2:3 → each TSA = 6a^2 → TSA ratio = 6a1^2 : 6a2^2 = a1^2:a2^2 → = 2^2:3^2 = 4:9. Lock in option A) 4:9. Trap-watch: option B) '2:3' doesn't hold - Surface area scales as the square of the edge ratio; option C) '8:27' doesn't hold - That cube ratio is for volumes, not surface areas.

Q2. Two cubes have their edges in the ratio 3:5. Working from edge to face to whole, the ratio of their total surface areas is?

• A.9:25
• B.3:5
• C.27:125
• D.6:10

Answer: A. 9:25

Spot-the-setup - a typical math numerical. The data on the table: 3, 5. We are after the quantity the stem asks for. Tool of choice - edge ratio = 3:5. Rearrange it for the unknown before substituting. Numbers in: edge ratio = 3:5 → each TSA = 6a^2 → TSA ratio = 6a1^2 : 6a2^2 = a1^2:a2^2 → = 3^2:5^2 = 9:25. Lock in option A) 9:25. Trap-watch: option B) '3:5' is incorrect: Surface area scales as the square of the edge ratio; option C) '27:125' doesn't hold - That cube ratio is for volumes, not surface areas.

Q3. Two cubes have their edges in the ratio 4:7. Working from edge to face to whole, the ratio of their total surface areas is?

• A.16:49
• B.4:7
• C.64:343
• D.8:14

Answer: A. 16:49

Given 4, 7, asked for the unknown. By edge ratio = 4:7. edge ratio = 4:7 → each TSA = 6a^2 → TSA ratio = 6a1^2 : 6a2^2 = a1^2:a2^2 → = 4^2:7^2 = 16:49. Therefore option A) 16:49. Others fail: option B) '4:7' fails since Surface area scales as the square of the edge ratio; option C) '64:343' is incorrect: That cube ratio is for volumes, not surface areas.