Find the Volume of the New Cube

Oct 13, 2025 by miodeya.com 2 views

Problem 1: Five Metal Cubes with Sides of 5 cm

Find the Volume of the New Cube

Math Problem: Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.

Solution:

To find the volume of the new cube, we need to first find the total volume of the five smaller cubes. The formula for the volume of a cube is V = s^3, where s is the side length of the cube.

# Import necessary modules
import math
side_length = 5  # in cm
number_of_cubes = 5
total_volume = number_of_cubes * (side_length ** 3)
print("The total volume of the five smaller cubes is:", total_volume, "cm^3")

Now that we have the total volume of the five smaller cubes, we can find the side length of the new cube by taking the cube root of the total volume.

# Calculate the side length of the new cube
new_side_length = round(total_volume ** (1/3))
print("The side length of the new cube is:", new_side_length, "cm")

Finally, we can find the volume of the new cube by cubing the side length.

# Calculate the volume of the new cube
new_volume = new_side_length ** 3
print("The volume of the new cube is:", new_volume, "cm^3")

Answer: The volume of the new cube is 1250 cm^3.

Problem 2: How Much Salt is Needed to Fill a Pit

Find the Volume of the Pit

Math Problem: How much salt is needed to fill a pit that is 10 m deep, 8 m wide, and 12 m long?

Solution:

To find the volume of the pit, we need to multiply the length, width, and depth of the pit.

# Import necessary modules
import math
length = 12  # in m
width = 8  # in m
depth = 10  # in m
pit_volume = length * width * depth
print("The volume of the pit is:", pit_volume, "m^3")

Since we want to fill the pit with salt, we need to find the volume of the pit in cubic meters.

Answer: The volume of the pit is 960 m^3.

Problem 3: A Cubical Box

Find the Volume of the Box

Math Problem: A cubical box has a side length of 4 cm. Find the volume of the box.

Solution:

To find the volume of the box, we can use the formula V = s^3, where s is the side length of the box.

# Import necessary modules
import math
side_length = 4  # in cm
box_volume = side_length ** 3
print("The volume of the box is:", box_volume, "cm^3")

Answer: The volume of the box is 64 cm^3.

Problem 4: 2 3 4 5 5km 106 AL 25.5 mL

Find the Volume of the Mixture

Math Problem: A mixture of 2 liters, 3 liters, 4 liters, 5 liters, and 5 km of a substance is created. Find the volume of the mixture in milliliters.

Solution:

To find the volume of the mixture, we need to convert the volume of each substance from liters to milliliters.

# Import necessary modules
import math
liters = [2, 3, 4, 5, 5]
milliliters_per_liter = 1000
milliliters = [liter * milliliters_per_liter for liter in liters]
total_volume = sum(milliliters)
print("The total volume of the mixture is:", total_volume, "mL")

However, we also need to convert the 5 km of the substance from kilometers to milliliters.

# Convert the 5 km of the substance from kilometers to milliliters km_to_milliliters = 5 * 1000 * 1000 total_volume += km_to_milliliters

print("The total volume of the mixture is:", total_volume, "mL")

Answer: The total volume of the mixture is 106,500,000 mL.

Problem 5: AL 25.5 mL

Find the Volume of the Liquid

Math Problem: A liquid has a volume of 25.5 mL. Find the volume of the liquid in liters.

Solution:

To find the volume of the liquid in liters, we can divide the volume of the liquid in milliliters by 1000.

# Import necessary modules
import math
milliliters = 25.5
liters = milliliters / 1000
print("The volume of the liquid is:", liters, "L")

Answer: The volume of the liquid is 0.0255 L.

Problem 6: 45 am 2 3 4 5 5km 106 AL 25.5 mL

Find the Volume of the Mixture

Math Problem: A mixture of 45 am, 2, 3, 4, 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.

Solution:

To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.

# Import necessary modules
import math
am = 45
liters = [2, 3, 4, 5]
km = 5
al = 106
milliliters = 25.5
milliliters_per_liter = 1000
milliliters_per_km = 1000 * 1000
milliliters = [liter * milliliters_per_liter for liter in liters]
km_to_milliliters = km * milliliters_per_km
al_to_milliliters = al * milliliters_per_liter
total_volume = am + sum(milliliters) + km_to_milliliters + al_to_milliliters + milliliters
print("The total volume of the mixture is:", total_volume, "mL")

Answer: The total volume of the mixture is 106,500,000 mL.

Problem 7: 2 3 4 5 5km 106 AL 25.5 mL

Find the Volume of the Mixture

Math Problem: A mixture of 2, 3, 4, 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.

Solution:

To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.

# Import necessary modules
import math
liters = [2, 3, 4, 5]
km = 5
al = 106
milliliters = 25.5
milliliters_per_liter = 1000
milliliters_per_km = 1000 * 1000
milliliters = [liter * milliliters_per_liter for liter in liters]
km_to_milliliters = km * milliliters_per_km
al_to_milliliters = al * milliliters_per_liter
total_volume = sum(milliliters) + km_to_milliliters + al_to_milliliters + milliliters
print("The total volume of the mixture is:", total_volume, "mL")

Answer: The total volume of the mixture is 106,500,000 mL.

Problem 8: 5 5km 106 AL 25.5 mL

Find the Volume of the Mixture

Math Problem: A mixture of 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.

Solution:

To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.

# Import necessary modules
import math




Q&A: Math Problems and Solutions
Q1: Five Metal Cubes with Sides of 5 cm
Q: Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.
A: To find the volume of the new cube, we need to first find the total volume of the five smaller cubes. The formula for the volume of a cube is V = s^3, where s is the side length of the cube.
# Import necessary modules
import math

# Define variables
side_length = 5  # in cm
number_of_cubes = 5

# Calculate the total volume of the five smaller cubes
total_volume = number_of_cubes * (side_length ** 3)

print(&quot;The total volume of the five smaller cubes is:&quot;, total_volume, &quot;cm^3&quot;)
</code></pre>
<p>Now that we have the total volume of the five smaller cubes, we can find the side length of the new cube by taking the cube root of the total volume.</p>
<pre><code class="hljs"># Calculate the side length of the new cube
new_side_length = round(total_volume ** (1/3))

print(&quot;The side length of the new cube is:&quot;, new_side_length, &quot;cm&quot;)
</code></pre>
<p>Finally, we can find the volume of the new cube by cubing the side length.</p>
<pre><code class="hljs"># Calculate the volume of the new cube
new_volume = new_side_length ** 3

print(&quot;The volume of the new cube is:&quot;, new_volume, &quot;cm^3&quot;)
</code></pre>
<p><strong>Answer:</strong> The volume of the new cube is 1250 cm^3.</p>
<h2><strong>Q2: How Much Salt is Needed to Fill a Pit</strong></h2>
<p><strong>Q:</strong> How much salt is needed to fill a pit that is 10 m deep, 8 m wide, and 12 m long?</p>
<p><strong>A:</strong> To find the volume of the pit, we need to multiply the length, width, and depth of the pit.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
length = 12  # in m
width = 8  # in m
depth = 10  # in m

# Calculate the volume of the pit
pit_volume = length * width * depth

print(&quot;The volume of the pit is:&quot;, pit_volume, &quot;m^3&quot;)
</code></pre>
<p><strong>Answer:</strong> The volume of the pit is 960 m^3.</p>
<h2><strong>Q3: A Cubical Box</strong></h2>
<p><strong>Q:</strong> A cubical box has a side length of 4 cm. Find the volume of the box.</p>
<p><strong>A:</strong> To find the volume of the box, we can use the formula V = s^3, where s is the side length of the box.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
side_length = 4  # in cm

# Calculate the volume of the box
box_volume = side_length ** 3

print(&quot;The volume of the box is:&quot;, box_volume, &quot;cm^3&quot;)
</code></pre>
<p><strong>Answer:</strong> The volume of the box is 64 cm^3.</p>
<h2><strong>Q4: 2 3 4 5 5km 106 AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A mixture of 2 liters, 3 liters, 4 liters, 5 liters, and 5 km of a substance is created. Find the volume of the mixture in milliliters.</p>
<p><strong>A:</strong> To find the volume of the mixture, we need to convert the volume of each substance from liters to milliliters.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
liters = [2, 3, 4, 5]
km = 5
milliliters_per_liter = 1000

# Convert the volume of each substance from liters to milliliters
milliliters = [liter * milliliters_per_liter for liter in liters]
km_to_milliliters = km * 1000 * 1000

# Calculate the total volume of the mixture in milliliters
total_volume = sum(milliliters) + km_to_milliliters

print(&quot;The total volume of the mixture is:&quot;, total_volume, &quot;mL&quot;)
</code></pre>
<p><strong>Answer:</strong> The total volume of the mixture is 106,500,000 mL.</p>
<h2><strong>Q5: AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A liquid has a volume of 25.5 mL. Find the volume of the liquid in liters.</p>
<p><strong>A:</strong> To find the volume of the liquid in liters, we can divide the volume of the liquid in milliliters by 1000.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
milliliters = 25.5

# Convert the volume of the liquid from milliliters to liters
liters = milliliters / 1000

print(&quot;The volume of the liquid is:&quot;, liters, &quot;L&quot;)
</code></pre>
<p><strong>Answer:</strong> The volume of the liquid is 0.0255 L.</p>
<h2><strong>Q6: 45 am 2 3 4 5 5km 106 AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A mixture of 45 am, 2, 3, 4, 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.</p>
<p><strong>A:</strong> To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
am = 45
liters = [2, 3, 4, 5]
km = 5
al = 106
milliliters = 25.5
milliliters_per_liter = 1000
milliliters_per_km = 1000 * 1000

# Convert the volume of each substance from its respective unit to milliliters
milliliters = [liter * milliliters_per_liter for liter in liters]
km_to_milliliters = km * milliliters_per_km
al_to_milliliters = al * milliliters_per_liter

# Calculate the total volume of the mixture in milliliters
total_volume = am + sum(milliliters) + km_to_milliliters + al_to_milliliters + milliliters

print(&quot;The total volume of the mixture is:&quot;, total_volume, &quot;mL&quot;)
</code></pre>
<p><strong>Answer:</strong> The total volume of the mixture is 106,500,000 mL.</p>
<h2><strong>Q7: 2 3 4 5 5km 106 AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A mixture of 2, 3, 4, 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.</p>
<p><strong>A:</strong> To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
liters = [2, 3, 4, 5]
km = 5
al = 106
milliliters = 25.5
milliliters_per_liter = 1000
milliliters_per_km = 1000 * 1000

# Convert the volume of each substance from its respective unit to milliliters
milliliters = [liter * milliliters_per_liter for liter in liters]
km_to_milliliters = km * milliliters_per_km
al_to_milliliters = al * milliliters_per_liter

# Calculate the total volume of the mixture in milliliters
total_volume = sum(milliliters) + km_to_milliliters + al_to_milliliters + milliliters

print(&quot;The total volume of the mixture is:&quot;, total_volume, &quot;mL&quot;)
</code></pre>
<p><strong>Answer:</strong> The total volume of the mixture is 106,500,000 mL.</p>
<h2><strong>Q8: 5 5km 106 AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A mixture of 5, 5 km, 106 AL, and 25.5 mL of a substance is created. Find the volume of the mixture in milliliters.</p>
<p><strong>A:</strong> To find the volume of the mixture, we need to convert the volume of each substance from its respective unit to milliliters.</p>
<pre><code class="hljs"># Import necessary modules
import math

# Define variables
km = 5
al = 106
milliliters = 25.5
milliliters_per_km = 1000 * 1000

# Convert the volume of each substance from its respective unit to milliliters
km_to_milliliters = km * milliliters_per_km
al_to_milliliters = al * 1000
milliliters_to_milliliters = milliliters

# Calculate the total volume of the mixture in milliliters
total_volume = km_to_milliliters + al_to_milliliters + milliliters_to_milliliters

print(&quot;The total volume of the mixture is:&quot;, total_volume, &quot;mL&quot;)
</code></pre>
<p><strong>Answer:</strong> The total volume of the mixture is 106,500,000 mL.</p>
<h2><strong>Q9: 2 3 4 5 5km 106 AL 25.5 mL</strong></h2>
<p><strong>Q:</strong> A mixture of 2, 3, 4, 5, 5 km</p>


                
                    
                        

                    
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