Question

the curved surface area of a hemisphere is 693 Cm square what is the volume of the hemisphere
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Answer 1

$\textbf{Given:}$

$\textsf{Curved surface area of hemisphere is 696 cm square}$

$\textbf{To find:}$

$\textsf{Volume of the hemisphere}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\textsf{Curved surface area of the hemisphere = 693 cm square}$

$\implies\mathsf{2\,\pi\,r^2=693}$

$\implies\mathsf{2{\times}\dfrac{22}{7}{\times}r^2=693}$

$\implies\mathsf{r^2=\dfrac{693{\times}7}{2{\times}22}}$

$\implies\mathsf{r^2=\dfrac{63{\times}7}{2{\times}2}}$

$\implies\mathsf{r^2=\dfrac{9{\times}7{\times}7}{2{\times}2}}$

$\implies\mathsf{r^2=\dfrac{3^2{\times}7^2}{2^2}}$

$\implies\mathsf{r=\dfrac{3{\times}7}{2}}$

$\implies\boxed{\mathsf{r=\dfrac{21}{2}}}$

$\textsf{Volume of hemisphere}$

$\mathsf{=\dfrac{2}{3}\pi\,r^3}$

$\mathsf{=\dfrac{2}{3}{\times}\dfrac{22}{7}{\times}\dfrac{21}{2}{\times}\dfrac{21}{2}{\times}\dfrac{21}{2}}$

$\mathsf{=22{\times}\dfrac{21}{2}{\times}\dfrac{21}{2}}$

$\mathsf{=22{\times}\dfrac{441}{4}}$

$\mathsf{=11{\times}\dfrac{441}{2}}$

$\mathsf{=\dfrac{4851}{2}}$

$\mathsf{=2425.5\,cm^2}$

$\textbf{Answer:}$

$\mathsf{Volume\;of\;the\;hemisphere\;is\;2425.5\;cm^2}$

$\textbf{Find more:}$

The total surface area of a solid hemisphere is 75 times the area of circle whose diameter is 6 cm what is the radius of the hemisphere ?

https://brainly.in/question/26688081