Question

If a sphere radius by 15% increase what effect on surface area?

Answer 1

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

$\green{\tt{\therefore{Increased\:T.S.A=1.076\pi r^{2}}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Radius \: of \: sphere ( r_{1} )= r \\ \\ \tt: \implies Increased \: radius( r_{2}) = r + 15\% \: of \: r \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Increased \: in \: T.S.A = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies T.S.A\: of \: sphere = 4\pi { r_{1} }^{2} \\ \\ \green{\tt: \implies T.S.A \: of \: sphere =4 \times \pi {r}^{2} } \\ \\ \tt \circ \: Increased \: Radii = r + \frac{15}{100} r \\ \\ \tt: \implies r_{2}= r + 0.15r \\ \\ \tt: \implies r_{2} =1.15 {r} \\ \\ \bold{New \: T.S.A \: of \: sphere} \\ \tt : \implies T.S.A \: of \: sphere = 4\pi { (r_{2})}^{2} \\ \\ \tt : \implies T.S.A\: of \: sphere = 4\pi \times {1.12r}^{2} \\ \\ \tt : \implies T.S.A \: of \: sphere = 4\pi \times 1.2544 {r}^{2} \\ \\ \tt : \implies T.S.A \: of \: sphere =5.0176\pi {r}^{2} \\ \\ \bold{Increased \:T.S.A\: of \: sphere} \\ \tt: \implies Increased \: T.S.A = 4\pi {( r_{2}) }^{2} - 4\pi {(r_{1})}^{2} \\ \\ \tt: \implies Increased \: T.S.A =5.0176\pi {r}^{2} - 4\pi {r}^{2} \\ \\ \green{\tt: \implies Increased \: T.S.A =1.0176\pi {r}^{2}}$

Answer 2

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$\boxed{Explained\:Answer}$

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