Assume you have a drop of 2 cm3 falling down. A) If the drop is a cube, what is its surface area? (Hint, volume of a cube = L3. Surface area of a cube=6*L2, where L is the length of the cube, and the factor of 6 as a cube has 6 faces). B) For the same drop, what is its surface area if it is a sphere? (Hint, volume of a sphere=4/3*pi*R³. Surface area of a sphere=4*pi*R?.) C) Find the surface area to volume ratios of both objects. Which object (sphere or cube) has a lower surface area to volume ratio? Which shape does the drop favor?

The planet Neptune is in the order of magnitude of 1023 m3. a. what is this in cubic kilometers? b. what is this in cubic miles? c. what is this in cubic centimeters?

In the diagram below there is a thick-walled cylindrical tube. Its height is H = 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2 = 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p x h?. R2 a) Proof that the proportionality constant k (p = kh?) is k = , ms 100m b) Determine the position of the center of mass of this object. c) Determine I, the moment of inertia of the cylindrical tube around the axle going through the center of the top (as shown on diagram). You can use lying =mr? (the rotational inertia of a ring of radius r and mass m rotating around an axis parallel to it, through its center).

What is the area of a circle which has a diameter equal to 3.138 cm? Hint The area is cm².

You purchased 5.2kg of apples from a store. You noticed that they used the smallest division of 4.2 g to weight them. What is the relative error of this weight measurement as a percentage. You want to calculate the area of your dorm which is in a rectangular shape. You measure the length and the width of the room as L= 4.8+(-.01) m, W= 4.4+(-.01) m. What is the absolute error in the area in m^2 units?

Soccer fields vary in size. A large soccer field is 144 meters long and 84.4 meters wide. Hint a. What are its dimensions in feet? o Its length is ft. o Its width is b. What are its dimensions in inches? o Its length is o Its width is ft. in. in.

Three vectors are given as: A = 3â – 9âỹ B = 7ââ + 10ŷ C = 4⣠+ 5ÿ+ 62 These three vectors are used to define a parallelepiped. (a) What is the volume of the parallelepiped? (b) What is the surface area of the parallelepiped?

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

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]

A right circular cylinder has a diameter of 1.1 in and a height of 8 ft. (a) What is the volume of the cylinder in cubic feet? .................... ft3(b) What is the volume in cubic meters? ................. m3(c) What is the volume in liters? ........................ L