Question

If radius of circle is tripled, then area of
circle will be increased by
(a) 100%
(b) 200%
(c) 400%
(d) 800%​

Answer 1

Answer:

• d) 800%

Given:-

• Radius of circle is tripled

To Find:-

• Area of circle will be increased by?

Step-by-step explanation:

→ Let the radius of circle be r unit

→ Then, the area is πr² sq•unit

→ Now, the radius is tripled,

→ Radius is = 3r unit

→ Area of circle is, π(3r)² sq• unit

The difference of area is,

$\implies \sf \: \pi {(3r)}^{2} - \pi {r}^{2}$

$\implies \sf \: \pi {r}^{2} (9 - 1)$

→ Now, area of circle is increased by cent,

$\implies \sf \dfrac{\pi {r}^{2}(9 - 1) }{\pi {r}^{2} } \times 100\%$

$\implies \sf \dfrac{8\pi {r}^{2} }{\pi {r}^{2} } \times 100\%$

$\implies \sf 8 \times 100\%$

$\implies \sf 800\%$

Answer 2

$\huge{\red{\sf{Given : }}}$

• Radius of the circle is tripled

$\huge{\blue{\sf{To\:find : }}}$

• increased Area of the circle

$\huge{\purple{\sf{Solution : }}}$

$:\implies{\sf {let\:the \:radius\: of \:the \:circle \:be \:R }}$

$\sf then , area = \pi r^2$

${\sf{Given , \:Radius\: is\: tripled .. :\implies radius\: is\: 3R }}$

$\sf {new \: area = \pi 3r^2}$

$\sf Increase \:in \: area = new \: area - original$

$\sf :\implies Increase \:in \: area = \pi3r^2 - \pi r ^ 2$

$\sf :\implies Increase \:in \: area = \pi r^2 (3-1)$

$\sf :\implies percentage \: increase \:in \: area = \frac {increased \: area}{original \: area} ×100%$

$\sf:\implies percentage \: increase \:in \: area =\frac {\pi r^2 (3-1)}{\pi r ^ 2}×100%$

$\sf:\implies percentage \: increase \:in \: area =\frac {2 \pi r^2 }{\pi r ^ 2}×100%$

$\sf:\implies percentage \: increase \:in \: area = 2× 100% = 200 %$

$\sf If \: radius \: of\: circle \: is \: tripled \: percentage \: increase \:in \: area \: is \: 200$%