What are the units of volume? Suppose another student tells you that a cylinder of radius r and height h has volume given by pir3h. Explain why this cannot be right.

T The total surface area, A, of the cylinder can be expressed as A = (a) Find the value of k. (b) Find the value of that makes the total surface area a minimum

Please help. This problem involves finding the radius and volume of a platinum atom using its density. Thank you.

An Olympic-size swimming pool is 50 m long, 25 m wide, and 2 m deep. In terms of volume, this pool, when full, holds how many kilogallons of water? Use the following equivalences: 1 gallon = 3.8 L     1 kilogallon = 103 gallon      1 L = 103 mL     for water: 1 mL = 1 cm3      1 m = 100 cm   [Numerical Problem: Just write the numerical answer without units. Express your answer to 2 significant figures in standard notation]

What is the unit-vector notation for each of the following vectors, all with magnitudes of 41.5? (a) Vector E with direction of 75.0° counterclockwise from the +x-axis. E= (b) Vector F with direction of 75.0° counterclockwise from the +y-axis. (c) Vector G with direction of 75.0° clockwise from the -y-axis. Need Help? Read It

You are making a sculpture that is a pyramid with a square base . You want the height of the pyramid to be 4 inches less than the length of a side of the base . You want the volume of the sculpture to be 200 cubic inches . a . Let x represent the length ( in inches ) of a side of the sculpture's base . Draw a diagram of the sculpture , and label the dimensions in terms of x . b . Write a function that gives the volume V of the sculpture in terms of x .

Iron has a density of 7.874 g/cm3, and the mass of a iron atom is 9.27 x 10-26 kg. (a) If the atoms are spherical and tightly packed, what is the volume of a iron atom? m³ (b) What is the distance between the centers of adjacent atoms? m

One of the most well-known equations in fluid mechanics is the Bernoulli equation. The standard form of the Bernoulli equation for incompressible irrotational fluid flow is (see pic below)(P is pressure, u is flow velocity of the fluid, z is the height of fluid relative to a reference line)a. Verify that each additive term in the Bernoulli equation has the samedimensions. b. What are the dimensions of the constant C?

A bacteria colony which is unrestricted in its growth will grow out in a circular manner. The population ?(?) of the colony at time t is directly proportional to the area of the circle. Suppose that a particular bacteria grows in such a way that the population is 1.3 times larger each day, and that initially (t=0) the colony has a diameter of 4 centimeter and a population of 7 million. a) Find the Population and Diameter of the colony on the fifth day. b) Find the Rate of Change of the Population and Diameter of the colony on the fifth day. c) Unrestricted growth models are often impractical as values will quickly become unreasonable. On what day does our model predict that the area of the bacteria colony will be 1 square mile?

Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]