Question
The surface area of a sphere is $2464cm^2$ lf its radius be doubled, what will be the surface area of the new sphere?
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Answer
Let the original radius be r.
⇒ original surface area $=4\pi\text{r}^2=2464\text{cm}^2\ ...(1)$
Given new radius $=2\text{r}$
⇒ New surface area $4\pi(2\text{r})^2$
$=4\times4\pi\text{r}^2$
$=4\times4\pi\text{r}^2$
$=4\times2464\ ...(\text{From}(1))$
$=9856\text{cm}^2$
⇒ original surface area $=4\pi\text{r}^2=2464\text{cm}^2\ ...(1)$
Given new radius $=2\text{r}$
⇒ New surface area $4\pi(2\text{r})^2$
$=4\times4\pi\text{r}^2$
$=4\times4\pi\text{r}^2$
$=4\times2464\ ...(\text{From}(1))$
$=9856\text{cm}^2$
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