Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much.
1. You are told that the volume of a sphere is given by V = pie d/4, where V is the volume and d is the diameter of the sphere. Is this equation dimensionally correct? (Use SI unit analysis to find out.)
2. The correct equation for the volume of a sphere is V = 4 pie r/3, where r is the radius of the sphere. Is the equation in exercise #20 correct? If not, what should it be when expressed in terms of d?
4. You often see 1 kg = 2.2 lb. This expression means that a) 1 kg is equivalent to 2.2 lb, b) this is a true equation, c) 1 lb = 2.2 kg, or d) none of the preceding?
5 a. If you wanted to express your height with the largest number, you would use 1) meters, 2) feet, 3) inches, or 4) centimeters? Why?
b. If you are 6.00 ft tall, what is your height in centimeters?
6. If the capillaries of an average adult were unwound and spread out end to end, they would extend to a length over 40 000 mi. If you are 1.75 m tall, how many times your height would the capillary length equal?
7. Suppose that when the United States goes completely metric, the dimensions of a football field are established as 100 m by 54 m. Which would be larger, the metric football field or a current football field, and what would be the difference between the areas?
8.The width and length of a room are 3.2 yd and 4.0 yd, respectively. If the height of the room is 8.0 ft, what is the volume of the room in a) cubic meters and b) cubic feet?
9. A compact disc (CD) has a diameter of approximately 12 cm. What is its area in m squared?
I use "^" to denote "power" or "exponent" operator.
1. Yes, dimensionally correct.
d is in meter (m); volume is in m^3; pi= 3.14 = no dimension
Left side is m^3; right side is (m)^3 = m^3
2. V = (4*pi*/3)*r^3
d = r/2
V = (4*pi*/3)*(d/2)^3 = ...
This solution is comprised of the necessary information and equations required to answer each of the physics based problems asked in this question. All formulas needed are provided.