Question

The volume of a cube is related to the area of a face by the formula V = A^3/2What is the volume of a cube whose face has an area of 100 cm??
helppp!!

Answer 1

Answer:

$\huge\boxed{1000 \ \text{cm}^3}$

Step-by-step explanation:

There are two ways we can solve this equation.

A) Using the formula provided

The formula provided states that the volume of a cube based on the area of one of it's faces will be $a^{\frac{3}{2}}$, a the area of one face. Since we know the area of one face, we can substitute that inside the equation.

$100^{\frac{3}{2}}$

It's important to note that when we have a number to a fraction power, it's the same as taking the denominator root of the base to the numerator power.

So - $100^{\frac{3}{2}}$ becomes $\sqrt{100^3}$

• $100^3=1000000$

• $\sqrt{1000000}=1000$

Therefore, the volume of this cube will be $1000 \ \text{cm}^3$

B) Using prior knowledge about cubes

We can additionally use prior knowledge to find the volume of this cube.

We know that the area of a square will be $s^2$, where s is the length of a side. We also know the formula to find the volume of a cube from it's side length is $s^3$.

Since we know that one face is 100, we can make an equation - $s^2=100$

• $\sqrt{s^2}=\sqrt{100}$
• $s=10$

Now that we know the value of s, we can plug it into the volume formula, $s^3$.

• $10^3$
• $10 \cdot 10 \cdot 10$
• $1000$

So the volume is $1000 \ \text{cm}^3$.

Hope this helped!