What Is The Height Of A Cylinder With A Volume Of $384 \pi$ Cubic Inches And A Radius Of 8 Inches? Round To The Nearest Tenth Of An Inch.$\square$ Inches

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What is the Height of a Cylinder with a Volume of 384Ï€384 \pi Cubic Inches and a Radius of 8 Inches?

In mathematics, a cylinder is a three-dimensional shape with two parallel and circular bases connected by a curved lateral surface. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder. In this article, we will discuss how to find the height of a cylinder with a given volume and radius.

The formula for the volume of a cylinder is V = πr²h. To find the height of the cylinder, we need to rearrange this formula to isolate h. We can do this by dividing both sides of the equation by πr², which gives us h = V / (πr²). This formula allows us to calculate the height of the cylinder given its volume and radius.

Now that we have the formula for the height of the cylinder, we can use it to calculate the height of the cylinder with a volume of 384Ï€384 \pi cubic inches and a radius of 8 inches. Plugging in these values into the formula, we get:

h = V / (πr²) h = 384π384 \pi / (π(8)²) h = 384π384 \pi / (64π) h = 6

Since we are asked to round the height to the nearest tenth of an inch, we need to examine the decimal part of the height. In this case, the height is exactly 6 inches, which means that it is already rounded to the nearest tenth.

In conclusion, the height of a cylinder with a volume of 384π384 \pi cubic inches and a radius of 8 inches is 6 inches. This is calculated using the formula h = V / (πr²), which allows us to find the height of the cylinder given its volume and radius.

The formula for the height of a cylinder can be used in a variety of real-world applications, such as:

  • Architecture: When designing buildings or other structures, architects need to calculate the height of cylinders to ensure that they are stable and safe.
  • Engineering: Engineers use the formula for the height of a cylinder to design and build pipes, tanks, and other cylindrical structures.
  • Science: Scientists use the formula for the height of a cylinder to calculate the volume of gases and liquids in cylindrical containers.

Here are some tips and tricks for working with the formula for the height of a cylinder:

  • Make sure to use the correct units: When calculating the height of a cylinder, make sure to use the correct units for the volume and radius. In this case, we used cubic inches and inches, respectively.
  • Check your calculations: Before rounding the height to the nearest tenth, make sure to check your calculations to ensure that they are accurate.
  • Use a calculator: If you are working with large numbers, it may be helpful to use a calculator to simplify the calculations.

Here are some common mistakes to avoid when working with the formula for the height of a cylinder:

  • Forgetting to use the correct units: Failing to use the correct units for the volume and radius can lead to incorrect calculations.
  • Rounding too early: Rounding the height to the nearest tenth too early can lead to incorrect results.
  • Not checking calculations: Failing to check calculations can lead to errors and incorrect results.

In conclusion, the height of a cylinder with a volume of 384π384 \pi cubic inches and a radius of 8 inches is 6 inches. This is calculated using the formula h = V / (πr²), which allows us to find the height of the cylinder given its volume and radius. By following the tips and tricks outlined in this article, you can ensure that your calculations are accurate and reliable.
Frequently Asked Questions (FAQs) about the Height of a Cylinder

A: The formula for the height of a cylinder is h = V / (πr²), where h is the height, V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the base.

A: To calculate the height of a cylinder, simply plug in the values for the volume and radius into the formula h = V / (πr²) and solve for h.

A: To find the height of the cylinder, plug in the values for the volume and radius into the formula h = V / (πr²). This gives us:

h = 256π256 \pi / (π(6)²) h = 256π256 \pi / (36π) h = 7.11

A: No, the formula for the height of a cylinder is h = V / (πr²), which means that it is used to find the height of a cylinder given its volume and radius. To find the volume of a cylinder, you would need to use the formula V = πr²h.

A: To find the volume of the cylinder, plug in the values for the height and radius into the formula V = πr²h. This gives us:

V = π(4)²(10) V = 160π V = 502.655

A: No, the formula for the height of a cylinder is h = V / (πr²), which means that it is used to find the height of a cylinder given its volume and radius. To find the radius of a cylinder, you would need to use the formula r = √(V / (πh)).

A: To find the radius of the cylinder, plug in the values for the height and volume into the formula r = √(V / (πh)). This gives us:

r = √(192π192 \pi / (π(8))) r = √24 r = 4.899

A: No, the formula for the height of a cylinder is h = V / (πr²), which means that it is used to find the height of a cylinder given its volume and radius. To find the surface area of a cylinder, you would need to use the formula A = 2πr² + 2πrh.

A: To find the surface area of the cylinder, plug in the values for the height and radius into the formula A = 2πr² + 2πrh. This gives us:

A = 2π(5)² + 2π(5)(12) A = 314.16 + 376.99 A = 691.15

In conclusion, the formula for the height of a cylinder is h = V / (πr²), which allows us to find the height of a cylinder given its volume and radius. By following the tips and tricks outlined in this article, you can ensure that your calculations are accurate and reliable.