Question

if the radius of a circle is tripled the area of circle will be increased by

Answer 1

$\large {\red {\underline {\overline {\mid {\sf {Aim:-{\mid }}}}}}}$

To find who many times the area of a circle will be increased if its radius is tripled.

$\large {\red {\underline {\overline {\mid {\sf {Prerequisite \: knowledge :-{\mid }}}}}}}$

$\small{\orange {\boxed {\bf {Area \: of \: a \: circle = πr² }}}}$

$\small{\orange {\boxed {\bf {Area∝Radius }}}}$

$\large {\red {\underline {\overline {\mid {\sf {Solution:-{\mid }}}}}}}$

$Let\: the\: radius\: of\: original \:circle\: be\: r$

$∴ Area\: of\: the \:circle = πr²$

$Now,\: radius \: becomes\: tripled \: i.e., 3r$

$Thus,\: area\: of\: the\: new \: circle = π(3r)²\\ =9πr²\\ =9×(original \: area)$

$Thus, \: we\: can\: say\: that\: the\: new\: area\: of \: the\: circle \: is \: 900%$

$Therefore, \: increased \: area = 900-100 \\= 800$

$\small{\orange {\boxed {\bf {d) 800}}}}$