Suppose you have a coffee mug with a cylindrical shape (the radius is uniform, in other words). What is its inside radius, in centimeters, if it holds 360 g of coffee when filled to a depth of 9.5 cm? Assume coffee has the same density as water, 1.00 g/cm3.
mass = volume x density
360g = volume x 1.00 g/cc
volume = 360 g/1.00 g/cc = 360 cc
volume of a cylinder = pi*r^2*h
v = 3.14 x r^2 * 9.5 cm
Solve for r
Show your work if you get stuck.
would the sig figs be 2 ?
To find the inside radius of the coffee mug, we can use the formula for the volume of a cylinder. The formula for the volume of a cylinder is given by V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, we are given the volume of the coffee as 360 g, and the depth to which the coffee is filled is 9.5 cm. We also know that the density of coffee is 1.00 g/cm³, which means that the volume of the coffee is equal to its mass.
Using the formula for the volume of a cylinder, we can write the equation as:
360 g = πr²(9.5 cm)
Now, we can solve for the inside radius (r).
Divide both sides of the equation by 9.5 cm:
360 g / 9.5 cm = πr²
Simplify:
38.0 g/cm = πr²
To solve for r, divide both sides of the equation by π:
(38.0 g/cm) / π = r²
Take the square root of both sides to get r:
r = √((38.0 g/cm) / π)
Now, we can calculate the value of r.
Substitute the given values into the equation:
r ≈ √((38.0 g/cm) / 3.1415)
Using a calculator, evaluate the expression:
r ≈ √(12.089 x 10.77 cm²)
r ≈ √(130.43143 cm²)
r ≈ 11.42 cm (rounded to two decimal places)
Therefore, the inside radius of the coffee mug is approximately 11.42 cm.