Question

The diameter of a sphere is decreased by 25%. By what percent does it’s curved surface
area decrease?
(himmat hai to easy steps mei solve karke dikhao)​

Answer 1

Answer:

the original curved surface area decreases by 43.75%.

Step-by-step explanation:

Answer 2

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

➝ Let the diameter of sphere be 100 cm.

$\pink{\bigstar}\:\:{\underline{\boxed{\bf\red{CSA\:of\:Sphere=4\pi{r}^{2}}}}}$

$\rm\longrightarrow\:CSA\:of\:sphere=4\pi\bigg(\dfrac{100}{2}\bigg)^2$

$\rm\longrightarrow\:CSA\:of\:sphere=\dfrac{\cancel{4}0000}{\cancel{4}}\pi\:c{m}^{2}$

$\rm\longrightarrow\:CSA\:of\:sphere=10000\pi\:c{m}^{2}$

⸕ Diameter is decreased by 25%,

• New Diameter = 100 - 25
• New Diameter = 75 cm

$\purple{\bigstar}\:\:{\underline{\boxed{\bf\pink{CSA\:of\:Sphere=4\pi{r}^{2}}}}}$

$\rm\longrightarrow\:CSA\:of\:sphere=4\pi\bigg(\dfrac{75}{2}\bigg)^2$

$\rm\longrightarrow\:CSA\:of\:sphere=\cancel{4}\pi\times\dfrac{5625}{\cancel{4}}$

$\rm\longrightarrow\:CSA\:of\:sphere=5625\pi\:c{m}^{2}$

$\rm\:Decrease\:in\:CSA\:of\:sphere=10000\pi-5625\pi$

$\rm\:Decrease\:in\:CSA\:of\:sphere=4375\pi\:c{m}^{2}$

$\rm\:Decrease\:\%\:of\:CSA\:of\:sphere=\dfrac{4375\pi}{10000\pi}\times\:100$

$\rm\:Decrease\:\%\:of\:CSA\:of\:sphere=43.75\%$

Hence,the curved surface area of sphere will be decreases by 43.75%.