Question

Please use detail steps to solve the problems.

1. The length and width of a rectangular room are measured to be 3.714 ± 0.005 m and 4.050 ± 0.005 m. Calculate the area of the room and its uncertainty in square meters. (Express your answers to the correct number of significant figures.)

a) Answer: area_____m^2

b) Answer: uncertainty_____m^2

2. What is the approximate number of galaxies in the known universe, assuming that the Milky Way has an average mass and that all of the mass in the known universe is in galaxies? The mass of the Milky Way is on the order of 1042 kg, and the mass of the known universe is about about 1053 kg.

Answer a) ______galaxies

Answer 1

length uncertainity width uncertainity : : : : l = 3.714 m al=0.005 m b = 4.050 m Ab = 0.005 m 1. a Since room contains of 6 sides which are of equal area. So, area of a one side : A= lxb = 3.714 x 4.050 m A = 15.042 m2 Mence area of room :- A = 64. = (6x 15.042) m2 A = 90.25 m² Answers Đ for uncertainity! maximum room arece: (A) mar = 6x Clese) x (b +Db) (A) max = 6x [ 3.714 +0.005] x [ 4.050 +0.005) m2 (A) max = 90.48 m² minimum room area! (A) min = 6x ce-sl) x (b- Db)

so, (A)min = 90.02 m2 uncertainity in area :- SA = (A) max - (A) min BA - 0.46 m2 Answes 42 average average mass of milky way : Mm = 10 kg. mass of universe: Mu = 1053 kg. so, approximated number of gala xies :- Mue n- Mm 1042 Answer approximated lo" galaxies in So there are known universe.