Question

A friend claims that if the radius of a pizza is doubled, then the area (The amount of pizza you get) doubles as well. Is the friend correct?

Answer 1

ANSWER

NO, the area is not doubled but multiplied by 4.

EXPLANATION

Given a pizza in a circular shape.

Area of a circular pizza

$Area\text{ \lparen without doubling the radius\rparen = }\pi\text{ r}^2$

When the radius is doubled

r' = 2r

$\begin{gathered} Area\text{ \lparen with doubled radius\rparen = }\pi\text{ \lparen2r\rparen}^2 \\ Area\text{ = 4 }\pi\text{ r}^2 \end{gathered}$

Hence, when the radius is doubled the area (The amount of pizza you get) is not doubled but multiplied by 4.