This is from wiley PLUS program and the green boxses are the

This is from wiley PLUS program and the green boxses are the ones I got it right but the red boxes are the ones I got it wrong. The website wants us to write it in exact sig fig so can you please help me with these THREE problems. ALL THREE PLEASE.

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 6.400 g, is pressed into a leaf of 4.720 m thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.800 m, what is the length of the fiber? (a) Number o.070 Unii (b) Number 1346

Solution

given density=19.32g/cm³

we know density= mass/ volume

(a) 19.32= (6.4/txA )     here txA represents volume

given t= 4.720 micrometer= 4.7x10^-6 meter=4.7x10^-4 cm

putting these values we get

19.32= (6.4/4.7x10^-4 xA)

A=( 6.4/19.32x4.7x10^-4 ) =0.07048458x10⁴ cm² =0.07048458m²

(b)we know the volume of cylinder= pi r² h

here h is length

so

19.32=6.4/pi x 2.8x10^-4 x2.8x10^-4 xh

h= (6.4/19.32x3.14x2.8x2.8x10^-8 ) =0.01345635x10⁸ cm=0.01345635x10⁶ m=13456.35m

(2) in c and d part the unit is gram /sec , not gram because it is rate of mass change not mass.

for the rate of mass change= dm/dt=4.6x0.8t^-0.2 -2.7+19

for part c we put t=2.0sec and for part d we put t=4.6 sec, and solving we get the answer.

(3) we know speed= distance/time

distance from sun to earth= 1.5x10⁸ km

light from sum to earth reaches in 8 min

so the speed in AU is distance/time =(1.5x10⁸ /8) = 0.1875x10⁸ AU/min