Question

the diameter of a circle is doubled.By how much does the area increase ?​

Answer 1

Answer:

By 4 times

Step-by-step explanation:

Suppose the diameter is 2d

the radius would be d

Area would be pie*d^2

Now the diameter is 4d

Radius would be 2d

Area would be pie*(2d)^2 = pie*4d^2

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Increased\:area=\frac{3\pi d^{2}}{4}}}}$

$\green{\tt{\therefore{Increased\%=300\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Diameter \: of \: circle = d \\ \\ \tt: \implies New \: diameter \: of \: circle= 2d \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Area \: increase = ?$

• According to given question :

$\circ \: \tt{Radius \: of \: circle = \frac{d}{2} } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: circle = \pi {r}^{2} \\ \\ \tt: \implies Area \: of \: circle = \pi { (\frac{d}{2} )}^{2} \\ \\ \tt: \implies Area \: of \: circle = \frac{ \pi{d}^{2} }{4} - - - - - (1) \\ \\ \circ \: \text{ Radius \: of \: new \: circle = d} \\ \\ \bold{For \: area \: of \: new \: circle} \\ \tt: \implies Area \: of \: new \: circle = \pi { r_{2} }^{2} \\ \\ \tt : \implies Area \: of \: new \: circle =\pi {d}^{2} - - - - - (2) \\ \\ \bold{For \: increase \: in \: area} \\ \tt: \implies Increased \: area =(2) - (1) \\ \\ \tt: \implies Increased \: area =\pi {d}^{2} - \frac{\pi {d}^{2} }{4} \\ \\ \tt: \implies Increased \: area = \frac{4\pi {d}^{2} - \pi {d}^{2} }{4} \\ \\ \green{\tt: \implies Increased \: area = \frac{3\pi {d}^{2} }{4}} \\ \\ \bold{For \: increased \: percent} \\ \tt: \implies Increase\% = \frac{Increased \: area}{Original \: area} \\ \\ \tt: \implies Increase\% = \frac{ \frac{3\pi {d}^{2} }{4} }{ \frac{\pi {d}^{2} }{4} } \\ \\ \tt: \implies Increase\% = \frac{3\pi {d}^{2} }{4} \times \frac{4}{\pi {d}^{2} } \times 100 \\ \\ \green{\tt: \implies Increase\% =300\%}$