Question

The volume of two cubes are 343:1331. Find the ratio of their edges. What is the ratio of their surface area

Answer 1

ratio of edges=7/11
and ratio of surface area= 6*7^2/6*11^2
.....=49/121

Answer 2

Concept:

Volume of a cube of edge length a is given by,

V = a³

Lateral Surface Area, LSA = 4a²

Total Surface Area, TSA = 6a²

Given:

The ratio of the volumes of two cubes is 343:1331.

Find:

The ratio of their edges and the ratio of their surface areas.

Answer:

The ratio of their edges is 7:11 and the ratio of their surface areas is 49:121.

Solution:

Let the edge of first cube be 'x' and the edge of second cube be y.

Volume of first cube, V₁ = x³

Volume of second cube, V₂ = y³

Ratio of volumes, V₁ : V₂ = 343:1331

V₁/V₂ = 343/1331

x³/y³ = (7×7×7)/(11×11×11)

(x/y)³ = 7³/11³

(x/y)³ = (7/11)³

x/y = 7/11                    ---------------------- (i)

x : y = 7 : 11

∴ Ratio of their edges = 7 : 11

Now, Total surface area of first cube, S₁ = 6x²

Total surface area of second cube, S₂ = 6y²

Ratio of their surface areas, S₁ : S₂ = 6x² : 6y²

S₁/S₂ = 6x²/6y²

S₁/S₂ = x²/y²

S₁/S₂ = (x/y)²

But (x/y) = 7/11              [From (i)]

∴ S₁/S₂ = (7/11)²

S₁/S₂ = 49/121

S₁:S₂ = 49:121

Hence, the ratio of their surface areas = 49 : 121.

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