Question

A cuboid whose ratio of length, breadth, and height are in the ratio of 1 ∶ 3 ∶ 9 have the same volume as a cube then what is the ratio of their surface area if the height of the cuboid is 18 cm? 

1. 27 ∶ 55 
2. 35 ∶ 41
3. 13 : 9
4. 56 ∶ 57

Answer 1

Correct Answer - Option 3 : 13 : 9

Given,

The sides ratio = 1 ∶ 3 ∶ 9

Formula used,

The volume of cube = a³

Calculation

From the question,

9R = 18 

⇒ R = 2

So, l  = 2 , b = 6, h = 18

⇒ 2 × 6 × 18  = a³

⇒ 6

The ratio of the surface the area  = 2 (lb +bh+ hl)/6a²

⇒ The ratio = 2(12 + 108 + 36)/(6 × 6²)

⇒ 312/216 

⇒ 52/36 = 26/18 = 13 : 9

∴ their surface Area ratio = 13 : 9