Answer:
(i) the cone will not overflow, as volume of cone is greater than volume of ice cream scoop
(ii) 80% of the cone will be filled if the ice cream scoop melts
Step-by-step explanation:
given, height of cone = 10 cm
and diameter = 4 cm ⇒ radius = 2 cm
diameter of spherical scoop = 4 cm ⇒ radius = 2 cm
(i) volume of sphere = [tex]\frac{4}{3}[/tex]πr³
volume of spherical scoop = [tex]\frac{4}{3}[/tex] × 3.14 × 2³ = 33.49 cm³
volume of cone = [tex]\frac{1}{3}[/tex]πr²h
volume of sugar cone = [tex]\frac{1}{3}[/tex] × 3.14 × 2² ×10 = 41.86 cm³
if the icecream melts into the cone, the cone will not overflow, as volume of cone is greater than volume of ice cream scoop
(ii) percentage of cone filled = [tex]\frac{33.49}{41.86}[/tex]× 100
= 80%
80% of the cone will be filled if the ice cream scoop melts