An ice cream cone has a radius of 3 cm and a height of 12 cm. A half scoop of ice cream is placed on the cone. If the ice cream melts, will it fit into the cone? [2 MARKS]

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Solution

Concept: 0.5 Mark
Formula: 0.5 Mark
Application: 1 Mark

Volume of a cone
$= \frac{1}{3} π r^{2} h$

$= \frac{1}{3} π (3)^{2} (12)$

$= 36 π c m^{3}$

Volume of a scoop
$= \frac{1}{2} \times \frac{4}{3} π r^{3}$

$= \frac{1}{2} \times \frac{4}{3} π (3)^{3}$

$= 18 π c m^{3}$

Since $18 π < 36 π$ , it will fit in the cone.

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An ice cream cone has a radius of 3 cm and a height of 12 cm. A half scoop of ice cream is placed on the cone. If the ice cream melts, will it fit into the cone? [2 MARKS]

Concept: 0.5 Mark Formula: 0.5 Mark Application: 1 Mark Volume of a cone =13πr2h =13π(3)2(12) =36π cm3 Volume of a scoop =12×43πr3 =12×43π(3)3 =18π cm3 Since 18π<36π, it will fit in the cone.