Question

The ratio of volume of two cube is 27:64.find the ratio of the their surface area.

Answer 1

given. ratio of vol .= 27/64
. a cube / b cube = (3) cube/(4) cube
therefore sides of cube (a) and cube (b) are 3 and 4 respectively.
hence the ratio of their surface areas are 6 a square / 6 b square.
I.e = 9/16

Answer 2

The ratio of the surface area is $9:16$.

Definition of ratio :

• A ratio in mathematics denotes the number of times one number contains another.
• In a bowl of fruit, for example, if there are eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Solution -

Given the ratio of volumes is $27:64$.

The volume of a cube of a side/volume of a cube of a side $= a^{3} / b^{3} = 27 : 64$.

$a/b = 3/4$

Now, the ratio of the surface area of a cube = surface area of a cube of side $a$ / surface area of a cube of side $b$.

$6a^{2} /6b^{2} \\a^{2} /b^{2} \\3^{2} /4^{2} \\9/16$

Therefore, The ratio of the surface area is $9/16$ that is  $9:16$.

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