Medical A typical prostate gland has a mass of about 20 g and is about the size
ID: 1273556 • Letter: M
Question
Medical A typical prostate gland has a mass of about 20 g and is about the size of a walnut. The gland can be modeled as a sphere 4.50 cm in diameter and of uniform density, What is the density of the prostate? Express your answer in g/cm3 and in standard SI units. How does the density compare to that of water? During a biopsy of the prostate, a thin needle is used to remove a series of cylindrical tissue samples. If the cylinders have a total length of 28.0 mm and a diameter of 0.100 mm, what is the total mass (in g) of tissue taken? What percentage of the mass of the prostate is removed during the biopsy? Medical The body mass index (BMI) estimates the amount of fat in a person's body. It is defined as the person's mass m in kg divided by the square of the person's height b in m. (a) Write the formula for BMI in terms of m and b. (b) In the United States, most people measure weight in pounds and height in feet and inches. Show that with weight in pounds and height h in inches, the BMI formula is BMI = 703 W/h2. (c) A person with a BMI between 25.0 and 30.0 is considered overweight. If a person is 5'11'' tall, foe what range of mass will he be considered overweight?Explanation / Answer
(a) density(d) = Mass/Volume
=> V = 4/3*(pi)*r^3
r = d/2 = 4.5/2cm = 2.25cm
V = 4/3*(3.14)*(2.25)^3 = 47.713 cm^3
d = m/v = 20/47.713 = 0.42 g/cm^3
In si 420 kg/m^3
(b) Less than the density of water
(c) V = (pi)*r^2*h = (pi)*(10^-1)^2*(2.8) = 8.8*10^-2 cm^3
m = V*d = 8.8*10^-2 * 0.42 = 3.7*10^-2 g
(d) Perrcentage of mass removed = 3.7*10^-2/20 *100 = 18.5%
(a) BMI = m/h2
(b) 1kg = 2.2 pounds
1 inch = 0.0254 m
=> BMI = 2.2W/(0.0254h)^2 = 703W/h^2
(c) 5'11'' = 1.8m
25 = m/1.8^2 => m = 81kg
30 = m/1.8^2 => m = 97.2kg
=> People with weight between 81 and 97.2 kgs would bne considered overweight.