Question

if the ratio of the sides of two cubes are 2 : 3 ,then the ratio of their surface area will be​

Answer 1

Answer:

4:9

Step-by-step explanation:

area is directly proportional to side²

S1:S2 = 2:3

then A1: A2 = (S1:S2)²

                  = (2:3)²

                  = 4:9

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Answer 2

the ratio of  surface area will be​ 4 : 9 if  ratio of the sides of two cubes are 2 : 3

Given:

• The ratio of the sides of two cubes are 2 : 3

To Find:

• Ratio of their surface area

Solution:

• Surface area of cube = 6a²
• Volume of cube = a³
• a = Side length of cube

Step 1:

Assume that side lengths of cubes are 2x  and 3x

Step 2:

Calculate Surface area of both cube

S₁ = 6(2x)² = 6x² (4)

S₂ =  6(3x)² = 6x² (9)

Step 3:

Find Ratio of surface Areas

S₁ / S₂  = 6x² (4) /   6x² (9)

S₁ / S₂  = 4 / 9   ( cancel 6x² )

4 : 9 is the ratio

Hence the ratio of their surface area will be​ 4 : 9