What is the maximum volume of the cylinder?

What is the maximum volume of the cylinder?

Therefore the volume is a maximum when 2r−2h+h=0, so h=2r and hr=2. Let the ratio of height to radius be ρ, then h=ρr. The volume of the cylinder is V=πr2h=πρr3.

How do you find the maximum volume of a cylinder in a sphere?

Let R be the radius of the sphere and let h be the height of the cylinder centered on the center of the sphere. By the Pythagorean theorem, the radius of the cylinder is given by r2=R2−(h2)2. The volume of the cylinder is hence V=πr2h=π(hR2−h34).

How do you find the maximum and minimum volume?

To find the maximum possible volume, add the greatest possible error to each measurement, then multiply. To find the minimum possible volume, subtract the greatest possible error from each measurement, then multiply.

What dimension of cylinder yields the largest volume?

Answer: The maximum volume occurs when r=1 ft and h=1 ft .

How do you find the dimensions of a cylinder if you know the volume?

The dimensions of a cylinder are determined by the restrictions on the volume, height, and diameter….Activity 1: Solving for the Height

1. Write the formula. Volume=π⋅radius2⋅height.
2. Substitute the dimensions of the shape into the formula. Use 3.14 as the value for π. 3,014.4=3.14⋅82⋅h.
3. Solve the equation for the variable.

How to maximize the surface area of a cylinder?

The surface area of the cylinder is then 2 × π r 2 + h × 2 π r cm 2. Solve equation (1) for h and substitute into equation (2). This will give an expression for the volume in terms of r alone. Use the calculus you know to maximize V.

How do you calculate the volume of a cylinder?

Square the radius of the cylinder. Multiply the square radius by pi and the cylinder’s height. Multiply the volume by the density of the cylinder. The result is the cylinder’s weight. How do you calculate the surface area to volume ratio of a cylinder? Find the volume of the cylinder using the formula πr²h.

How to find the volume of a right trapezoidal cylinder?

How do you find the volume of a right trapezoidal cylinder? A right trapezoidal cylinder, also known as a rectangular prism, can be solved as such: Add the two parallel sides (bases) of the trapezium together. Divide the result by 2. Multiply the result of step 2 by the height of the trapezium (i.e., the distance that separates the two sides).

How to calculate surface area to volume ratio?

How do you calculate the surface area to volume ratio of a cylinder? Find the volume of the cylinder using the formula πr²h. Find the surface area of the cylinder using the formula 2πrh + 2πr2. Make a ratio out of the two formulas, i.e. πr 2 h : 2πrh + 2πr 2. Alternatively, simplify it to rh : 2 (h+r).