Question

Joseph kept 26 cards in a cap,bearing one english alphabet on each card. one card is drawn at random. what is the probability that the card drawn is a vowel card?​

Answer 1

Solution:

(i) Cost of white-washing the dome from inside = Rs 4989.60

Cost of white-washing 1m2 area = Rs 20

CSA of the inner side of dome = 498.96/2 m^2 = 249.48 m^2

(ii) Let the inner radius of the hemispherical dome be r.

CSA of inner side of dome = 249.48 m^2 (from (i))

Formula to find CSA of a hemi sphere = 2πr^2

2πr2 = 249.48

2×(22/7)×r2 = 249.48

r^2 = (249.48×7)/(2×22)

r^2 = 39.69

r = 6.3

So, radius is 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

Using formula, volume of the hemisphere = 2/3 πr^3

= (2/3)×(22/7)×6.3×6.3×6.3

= 523.908

= 523.9(approx.)

Answer: Volume of air inside the dome is 523.9 m^3.