Question

The mass of a cylinder made of barium with a height of 2 inches depends on the radius of the cylinder as defined by the function m(r)=7.188. Which system of equations and solution can be used to represent the radius if the mass of the cylinder is 11,000 grams? Round to the nearest hundredth of an inch.

Answer 1

Answer:

$r=22.07\ in$

Step-by-step explanation:

The correct function is

$m(r)=7.188\pi r^{2}$

we have

System of equations

$m=7.188\pi r^{2}$ -----> equation A

$m=11,000$ -----> equation B

Solve by substitution method

substitute equation B in equation A

$11,000=7.188\pi r^{2}$

Solve for r

Divide by 7.188π both sides

$r^{2}=\frac{11,000}{7.188\pi}$

square root both sides

$r=22.07\ in$

Answer 2

$m(r)=7.188*\pi*r^2$ system of equations and solution can be used to represent the radius if the mass of the cylinder is 11,000 grams

Explanation:

The cylinder is one of the most basic curved geometric shapes, with the surface formed by points at a fixed distance from given line segment as the  the axis cylinder.

The mass of the cylinder = 11,000 gram

Height of the cylinder = 2 inches. Height is the measure of vertical distance, either vertical extent or vertical position.

$m(r)=7.188*\pi*r^2$ it means the mass of the cylinder as the function of radius. Radius is any of the line segments from its center to its perimeter, and in more modern usage and it is also their length.

$m=11000$

$11000 = 7.188*\pi*r^2 \\r^2 = 1530.328\\r=21.215 in$  therefore

We need to round  r to the nearest hundredth of an inch. To round to the nearest cent, nearest penny or nearest hundredth, you will need to locate the hundredths place. Therefore the answer is r=21.22 inch and the equations (an equation is a mathematical sentence that has two equal sides separated by the equal sign) and solution that can be used to represent the radius if the mass of the cylinder is 11000 grams is $m(r)=7.188*\pi*r^2$

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