Question

28.
Two cubes have volumes in the ratio 27 : 216. What
is the ratio of the area of the face of one cube to that
of the other cube?
A. 1:4
B. 1:6
C. 1:9
D. 1:18​

Answer 1

Dear Students,

● Answer -

(A) 1:4

◆ Explaination -

Let s1 and s2 be sides of two cubes.

Ratio of volumes of cubes of two cubes are -

V1/V2 = (l1/l2)³

27/216 = (l1/l2)³

l1/l2 = ∛(27/216)

l1/l2 = 3/6

l1/l2 = 1/2

Ratio of areas of faces of two cubes is -

A1/A2 = (l1/l2)²

A1/A2 = (1/2)²

A1/A2 = 1/4

Thanks dear. Hope this helps you...

Answer 2

Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Ratio of volumes = 27:216

So, As we know that

$\dfrac{27}{216}=\dfrac{S_1^3}{S_2^3}\\\\\dfrac{3^3}{6^3}=\dfrac{S_1^3}{S_2^3}\\\\\dfrac{S_1}{S_2}=\dfrac{3}{6}=\dfrac{1}{2}$

So, Ratio of the area of the face of one cube to that of the other cube :

$\dfrac{S_1^2}{S_2^}=\dfrac{1^2}{2^2}=\dfrac{1}{4}$

Hence, Option 'A' is correct.

# learn more:

Two cubes have volumes in the ratio 27 is to 216 what is the ratio of the area of the face of the one cube to that of the other cube?

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