Question

The volume of a cube is a perfect square. If the side length of the cube is a single digit integer, what will
the maximum surface area of the cube (in mnº)?
A 96
B 216
C 384
D 486​

Answer 1

Answer:

Volume of a cube is equal to (side)^3 since it is a perfect square and side is single digit no. the side is equal to 4

Step-by-step explanation:

As 4^3 is 64 and it is perfect square, now the surface area of cube = 6* side^2  =6* 16= 96

Option A

Answer 2

Answer:

The maximum surface area of the cube = 486 square units

Step-by-step explanation:

Given,

The volume of a cube is a perfect square.

The length of a side of a cube is a single digit number.

To find,

The maximum surface area of the cube.

Solution

Recall the formula,

The volume of the cube = a³

The surface area of the cube = 6a²

Since the length of the side of the cube is a single digit number, the length of the side of the cube can be 1,2,3,4,5,6,7,8,9

The possible volume of the cube i the cubes of all the single digit numbers. They are 1,8,27,64,125,216,343,512,729

Since it is given that the volume is a perfect square, perfect square numbers in the above numbers are 1,64,729

∴ The possible volume of the cube which is perfect squares = 1, 64, 729

Out of these the maximum length of the side of the cube  = 9

Hence maximum surface area = 6a² = 6 ×81 = 486

∴ The maximum surface area of the cube = 486 square units

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