The volume of a cube is 9261000 `m^(2)`
If the volume of the cube is increased by 1387000 `m^(3)` then the new side of the cube is

Options

A. 250 m
B. 200 m
C. 210 m
D. 220 m

Answer

To find the new side of the cube after the volume is increased, we can follow these steps:

### Step 1: Calculate the new volume of the cube
The original volume of the cube is given as 9261000 m³. The volume is increased by 1387000 m³.

\[ \text{New Volume} = \text{Original Volume} + \text{Increase in Volume} \]
\[ \text{New Volume} = 9261000 + 1387000 = 10648000 \, m^3 \]

### Step 2: Set up the equation for the volume of the cube
Let the new side of the cube be \( s \). The volume of a cube is given by the formula:

\[ \text{Volume} = s^3 \]

So we can write:

\[ s^3 = 10648000 \, m^3 \]

### Step 3: Calculate the cube root to find the new side length
To find \( s \), we need to calculate the cube root of the new volume:

\[ s = \sqrt[3]{10648000} \]

### Step 4: Simplify the cube root
We can express 10648000 in a more manageable form:

\[ 10648000 = 10648 \times 1000 \]

Now we can break it down further:

\[ 10648 = 22^3 \times 10^3 \]

Thus, we can write:

\[ 10648000 = (22 \times 10)^3 \]

### Step 5: Find the new side length
Now we can find \( s \):

\[ s = \sqrt[3]{(22 \times 10)^3} = 22 \times 10 = 220 \, m \]

### Final Answer
The new side of the cube is \( 220 \, m \).

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