Let the radius of the sphere be Then its DIAMETER = Curved SURFACE area of the ORIGINAL sphere ⠀⠀:New diameter(decreased) of the sphere⠀:⠀⠀: Radius of the new sphere: New curved surface area

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The diameter of a sphere is decreased by 25percent.By what,t per cent does its curved surface area decrease?

Political Science Secondary School in Political Science 10 months ago

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

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

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

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 of 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%.

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Posted on 25 Oct 2024, this text provides information on Political Science related to Secondary School in Political Science. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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The diameter of a sphere is decreased by 25percent.By what,t per cent does its curved surface area decrease?