Formula for the Volume of a Rectangular Block

Oct 13, 2025 by windailys.com 123 views

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Introduction

The volume of a block of wood is given as $$1440 , \text{cm}^3$$. We are also provided with the length and breadth of the block, which are $15 \, \text{cm}$ and $12 \, \text{cm}$ , respectively. In this article, we will use the formula for the volume of a rectangular block to find the height of the block.

Formula for the Volume of a Rectangular Block

The formula for the volume of a rectangular block is given by:

V = l \times b \times h

where $V$ is the volume, $l$ is the length, $b$ is the breadth, and $h$ is the height.

Given Values

We are given the following values:

Volume ( $V$ ) = $$1440 , \text{cm}^3$$
Length ( $l$ ) = $15 \, \text{cm}$
Breadth ( $b$ ) = $12 \, \text{cm}$

Finding the Height

We can use the formula for the volume of a rectangular block to find the height. Rearranging the formula to solve for $h$ , we get:

h = \frac{V}{l \times b}

Substituting the given values, we get:

h = \frac{1440}{15 \times 12}

Calculating the Height

To calculate the height, we need to perform the multiplication and division operations.

h = \frac{1440}{180}

h = 8

Conclusion

Therefore, the height of the block of wood is $8 \, \text{cm}$ .

Real-World Applications

The concept of finding the height of a rectangular block is used in various real-world applications, such as:

Architecture: In building design, architects need to calculate the height of walls, ceilings, and other structural elements to ensure that they are proportional and aesthetically pleasing.
Engineering: Engineers use the concept of volume and height to design and build structures such as bridges, tunnels, and buildings.
Manufacturing: Manufacturers use the concept of volume and height to design and build products such as boxes, containers, and packaging materials.

Example Problems

Here are some example problems that involve finding the height of a rectangular block:

A rectangular block has a volume of $$2000 , \text{cm}^3$$ and a length of $20 \, \text{cm}$ . If the breadth is $10 \, \text{cm}$ , find the height.
A rectangular block has a volume of $$3000 , \text{cm}^3$$ and a breadth of $15 \, \text{cm}$ . If the length is $20 \, \text{cm}$ , find the height.

Solutions to Example Problems

Here are the solutions to the example problems:

A rectangular block has a volume of $$2000 , \text{cm}^3$$ and a length of $20 \, \text{cm}$ . If the breadth is $10 \, \text{cm}$ , find the height.

h = \frac{2000}{20 \times 10}

h = \frac{2000}{200}

h = 10

A rectangular block has a volume of $$3000 , \text{cm}^3$$ and a breadth of $15 \, \text{cm}$ . If the length is $20 \, \text{cm}$ , find the height.

h = \frac{3000}{20 \times 15}

h = \frac{3000}{300}

h = 10

Conclusion

In conclusion, the concept of finding the height of a rectangular block is an important one in mathematics and has various real-world applications. By using the formula for the volume of a rectangular block, we can easily find the height of a block given its volume and dimensions.

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Introduction

In our previous article, we discussed how to find the height of a rectangular block given its volume and dimensions. In this article, we will answer some frequently asked questions related to the volume of a block of wood.

Q: What is the formula for the volume of a rectangular block?

A: The formula for the volume of a rectangular block is given by:

V = l \times b \times h

where $V$ is the volume, $l$ is the length, $b$ is the breadth, and $h$ is the height.

Q: How do I find the height of a rectangular block if I know its volume and dimensions?

A: To find the height of a rectangular block, you can use the formula:

h = \frac{V}{l \times b}

Q: What if I only know the length and breadth of a rectangular block, but not its volume?

A: If you only know the length and breadth of a rectangular block, you can use the formula:

V = l \times b \times h

to find the volume, and then use the formula:

h = \frac{V}{l \times b}

to find the height.

Q: Can I use the formula for the volume of a rectangular block to find the volume of a cube?

A: Yes, you can use the formula for the volume of a rectangular block to find the volume of a cube. Since a cube has equal length, breadth, and height, you can use the formula:

V = l \times l \times l

V = l^3

Q: What if I have a rectangular block with a volume of $$1000 , \text{cm}^3$$ and a length of $10 \, \text{cm}$ ? If the breadth is $5 \, \text{cm}$ , what is the height?

A: To find the height, you can use the formula:

h = \frac{V}{l \times b}

Substituting the given values, you get:

h = \frac{1000}{10 \times 5}

h = \frac{1000}{50}

h = 20

Q: Can I use the formula for the volume of a rectangular block to find the volume of a sphere?

A: No, you cannot use the formula for the volume of a rectangular block to find the volume of a sphere. The formula for the volume of a sphere is given by:

V = \frac{4}{3} \pi r^3

where $r$ is the radius of the sphere.

Q: What if I have a rectangular block with a volume of $$500 , \text{cm}^3$$ and a breadth of $10 \, \text{cm}$ ? If the length is $5 \, \text{cm}$ , what is the height?

A: To find the height, you can use the formula:

h = \frac{V}{l \times b}

Substituting the given values, you get:

h = \frac{500}{5 \times 10}

h = \frac{500}{50}

h = 10

Conclusion

In conclusion, the formula for the volume of a rectangular block is a useful tool for finding the height of a block given its volume and dimensions. By using the formula, you can easily find the height of a block and solve various problems related to the volume of a block of wood.

Real-World Applications

The concept of finding the height of a rectangular block is used in various real-world applications, such as:

Architecture: In building design, architects need to calculate the height of walls, ceilings, and other structural elements to ensure that they are proportional and aesthetically pleasing.
Engineering: Engineers use the concept of volume and height to design and build structures such as bridges, tunnels, and buildings.
Manufacturing: Manufacturers use the concept of volume and height to design and build products such as boxes, containers, and packaging materials.

Example Problems

Here are some example problems that involve finding the height of a rectangular block:

A rectangular block has a volume of $$2000 , \text{cm}^3$$ and a length of $20 \, \text{cm}$ . If the breadth is $10 \, \text{cm}$ , find the height.
A rectangular block has a volume of $$3000 , \text{cm}^3$$ and a breadth of $15 \, \text{cm}$ . If the length is $20 \, \text{cm}$ , find the height.

Solutions to Example Problems

Here are the solutions to the example problems:

A rectangular block has a volume of $$2000 , \text{cm}^3$$ and a length of $20 \, \text{cm}$ . If the breadth is $10 \, \text{cm}$ , find the height.

h = \frac{2000}{20 \times 10}

h = \frac{2000}{200}

h = 10

A rectangular block has a volume of $$3000 , \text{cm}^3$$ and a breadth of $15 \, \text{cm}$ . If the length is $20 \, \text{cm}$ , find the height.

h = \frac{3000}{20 \times 15}

h = \frac{3000}{300}

h = 10