Question

if the radus of a sphere is increased by 5cm, then its surface area is increases by 704cm sq. the radius the sphere before theincreasewas

Answer 1

$$\begin{gathered} \text{Let r be the radius of the original sphere.} \\ \text{So, surface area of original sphere}=4{\mathrm{\pi r}}^2 \\ \mathrm{Now},\mathrm{radius}\mathrm{is}\mathrm{increased}\mathrm{by}5\mathrm{cm}\mathrm{and}\mathrm{suface}\mathrm{area}\mathrm{is}\mathrm{increased}\mathrm{by}704{\mathrm{cm}}^2.\mathrm{Therefore}, \\ \mathrm{Surface}\mathrm{area}=\mathrm{original}\mathrm{surface}\mathrm{area}+704 \\ \Rightarrow 4\mathrm{\pi }{\left(\mathrm{r}+5\right)}^2=4{\mathrm{\pi r}}^2+704 \\ \Rightarrow 4\mathrm{\pi }{\left(\mathrm{r}+5\right)}^2=4{\mathrm{\pi r}}^2+4\mathrm{\pi }\times 56 \\ \Rightarrow {\left(\mathrm{r}+5\right)}^2-{\mathrm{r}}^2-56=0 \\ \Rightarrow 25+10\mathrm{r}-56=0 \\ \Rightarrow 10\mathrm{r}=31 \\ \Rightarrow \mathrm{r}=3.1\mathrm{cm} \\ \mathrm{Hence},\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{original}\mathrm{shere}\mathrm{is}3.1\mathrm{cm}. \end{gathered}$$