A hemispherical bowl is 264 cm round at the brim. Suppose that the bowl is half-full of beverage. If the beverage is served in hemispherical glasses 6 cm in the diameter at the top, how many people would be served?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1372.
The circumference of a circle = 2πR
⇒ 264 = 2 × 22/7 × R
⇒ 264 = 44R/7 ⇒ R = (264 × 7)/44 = 1848/44 = 42 cm
V = 2/3πR3 = 2/3 × 22/7 × 423 = 77664 cm3
Diameter = 6 cm ⇒ Radius = 3 cm
Vglass = 2/3πr3 = 2/3⋅22/7⋅33 = 44/7⋅9 = 396/7 cm3
Number = 77664 × 7/396 ≈ 1372