If the Total Surface Area of a Cube is 24, What is the Volume of the Cube? GMAT Problem Solving

Question: If the total surface area of a cube is 24, what is the volume of the cube?

1. 8
2. 24
3. 64
4. 48√6
5. 216

‘If the total surface area of a cube is 24, what is the volume of the cube?.' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1

 It is asked If the total surface area of a cube is 24, what is the volume of the cube?
Evaluating further –
Total surface area of a cube is 6\(a^2 \)

This means

24=\(6a^2\)

=24/6=\(a^2\)

= 4 = \(a^2\)

= 2 = a
So, now we know that The value of a is 2.
Now,
Formula for Volume of cube= a3

= \(a^3\)

=8
The answer is A which is 8.

Correct Answer: A

Approach Solution 2

There is another approach to answering this question: what is the volume of the cube? If It is asked If the total surface area of a cube is 24,
Total surface area of a cube is \(6a^2\)

Here a is length ,
This means

24= \(6a^2\)

=24/6= \(a^2\)

= 4 = \(a^2\)

= -2 or 2 = a

So, now we know that The value of a is -2 or 2.
we'll get -2 and 2 , but since only we consider +ve as we can't have any -ve side

We take a = 2

since this is a cube all sides are equal
Volume = length x breadth x height
= 2*2*2 = 8

The answer is A which is 8.

Correct Answer: A

Approach Solution 3

This problem can be solved with easy and time saving method.
Total surface area of cube is (6a^2)

So, 24=6a^2

that implies 24/6=a^2
that implies4=a^2
that implies2=a

So, the value of a is 2.
Now, the volume of cube=a^3
that implies 2^3 =8

Correct Answer: A

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