Rewrite the volume formula to create an equation that can be used to calculate the radius, [tex]$r$[/tex], of the water tank.
Drag the terms to the correct locations in the equation. Not all terms will be used.
[tex]r=\sqrt{\frac{1+\ldots \ldots \ldots \ldots}{1}}[/tex]
h
[tex]400 \pi h[/tex]
20 V
V
[tex]20 h[/tex]
[tex]20 \pi[/tex]
Answer (2)
To find the radius r of a cylindrical water tank using its volume V and height h , we start with the formula V = π r 2 h . Rearranging gives r = πh V , and to match the required format, we express it as r = 20 πh 20 V . The terms to fill in the blanks are 20 V for the numerator and 20 πh for the denominator.
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Recall the formula for the volume of a cylinder: V = π r 2 h .
Divide both sides of the equation by πh to get r 2 = πh V .
Take the square root of both sides to solve for r : r = πh V .
Multiply the numerator and denominator by 20 to match the required format: r = 20 πh 20 V .
Explanation
Recall the volume formula Let's start by recalling the formula for the volume of a cylinder, which is:
V = π r 2 h
where:
V is the volume,
r is the radius,
h is the height.
Divide by πh Our goal is to isolate r on one side of the equation. To do this, we'll first divide both sides of the equation by πh :
πh V = πh π r 2 h
πh V = r 2
Take the square root Now, to solve for r , we take the square root of both sides of the equation:
πh V = r 2
r = πh V
Multiply by 20/20 To match the required format, we can multiply both the numerator and the denominator inside the square root by 20:
r = 20 πh 20 V
Examples
Understanding how to calculate the radius of a cylindrical water tank is crucial in many practical scenarios. For instance, if you know the volume of water needed for a community and the height of the tank due to space constraints, you can use this formula to determine the required radius of the tank. This ensures that the tank can hold the necessary volume of water while fitting within the available space. Similarly, in industrial applications, knowing the volume and desired height of a cylindrical storage container allows engineers to calculate the precise radius needed for efficient storage and transportation of materials.
