Question

plzzz solve it.... ​

Answer 1

$\large{\underbrace{\sf{\red{Answer:}}}}$

$\huge{\boxed{\sf{\orange{ 43 \dfrac{3}{4} \% \:or\: 43.75 \%}}}}$

$\large{\underbrace{\sf{\purple{Explanation:}}}}$

Let the radius of the sphere be $\displaystyle{\sf{ \dfrac{ \pi}{2}cm.}}$

Then its diameter = $\implies{\sf{ \big( \dfrac{ \pi}{2} \big) cm.}}$

Curved surface area off the original sphere

⠀⠀:$\implies{\sf{ 4 \pi \dfrac{r}{2}^{2} = \pi r^{2}cm^{2}}}$

New diameter(decreased) of the sphere

⠀:$\implies{\sf{ r-r \times \dfrac{25}{100}}}$

⠀⠀:$\implies{\sf{ r- \dfrac{r}{4}= \dfrac{3r}{4}}}$

${ \therefore}$ Radius of the new sphere

:$\implies{\sf{ \dfrac{1}{2} \big( \dfrac{3r}{4} \big) = \frac{3r}{8}cm }}$

${ \therefore}$ New curved surface area of the sphere

:$\implies{\sf{ 4\pi \big( \frac{3r}{8}cm \big) = \dfrac{9\pi r^{2}}{16}cm^{2}}}$

${ \therefore}$ Decrease in the original curved surface area

:$\implies{\sf{ \pi r^{2} - \dfrac{9 \pi r^{2}}{16}}}$

:$\implies{\sf{ \pi r^{2} - \dfrac{7 \pi r^{2}}{16}}}$

${ \therefore}$ Percentage of decrease in the original curved surface area

:$\implies{\sf{ \dfrac{\dfrac{7 \pi r^{2}}{16}}{ \pi r^{2}} \times 100 \%}}$

$\large{:}\implies{\boxed{\sf{\pink{ 43 \dfrac{3}{4} \%\:or\:43.75 \%}}}}$

Hence, the original curved surface area decreases by 43.75%.

Answer 2

$\large{\underbrace{\sf{\red{Answer:}}}}$

$\huge{\boxed{\sf{\orange{ 43 \dfrac{3}{4} \% \:or\: 43.75 \%}}}}$

$\large{\underbrace{\sf{\purple{Explanation:}}}}$

Let the radius of the sphere be $\displaystyle{\sf{ \dfrac{ \pi}{2}cm.}}$

Then its diameter = $\implies{\sf{ \big( \dfrac{ \pi}{2} \big) cm.}}$

Curved surface area off the original sphere

⠀⠀:$\implies{\sf{ 4 \pi \dfrac{r}{2}^{2} = \pi r^{2}cm^{2}}}$

New diameter(decreased) of the sphere

⠀:$\implies{\sf{ r-r \times \dfrac{25}{100}}}$

⠀⠀:$\implies{\sf{ r- \dfrac{r}{4}= \dfrac{3r}{4}}}$

${ \therefore}$ Radius of the new sphere

:$\implies{\sf{ \dfrac{1}{2} \big( \dfrac{3r}{4} \big) = \frac{3r}{8}cm }}$

${ \therefore}$ New curved surface area of the sphere

:$\implies{\sf{ 4\pi \big( \frac{3r}{8}cm \big) = \dfrac{9\pi r^{2}}{16}cm^{2}}}$

${ \therefore}$ Decrease in the original curved surface area

:$\implies{\sf{ \pi r^{2} - \dfrac{9 \pi r^{2}}{16}}}$

:$\implies{\sf{ \pi r^{2} - \dfrac{7 \pi r^{2}}{16}}}$

${ \therefore}$ Percentage of decrease in the original curved surface area

:$\implies{\sf{ \dfrac{\dfrac{7 \pi r^{2}}{16}}{ \pi r^{2}} \times 100 \%}}$

$\large{:}\implies{\boxed{\sf{\pink{ 43 \dfrac{3}{4} \%\:or\:43.75 \%}}}}$

Hence, the original curved surface area decreases by 43.75%.