# Surface Area ad Volume of A Sphere - Class 9 : Notes

(1) The set of all points in space which are equidistant the fixed point is called a sphere. The fixed point is called the center of the sphere and the constant distance is called its radius.(2) For a sphere of radius r, Â we have
(i) Â Surface area $= 4\pi{r^2}$
For Example:Â If radius $r = 5cm$ then
Surface area $= 4\pi \times {5^2} = 314c{m^2}$

(ii) Volume $= {4 \over 3}\pi {r^3}$
For Example:Â If radius $r = 5cm$ then
Volume $= \frac{4}{3}\pi \times {5^3} = 523.33c{m^3}$

(3) Curved surface area of a hemisphere of radius r is $2\pi {r^2}$
For Example:Â If a radius of hemisphere is $5cm$, then
Curved surface area of a hemisphere is $2\pi \times {5^2} = 157c{m^2}$

(4) Total surface area of a hemisphere of radius r is $3\pi {r^2}$
For Example:Â If a radius of hemisphere is $5cm$, then
Total surface area of a hemisphere is $3\pi \times {5^2} = 235.5c{m^2}$

(5) Volume of a hemisphere of radius r is ${2 \over 3}\pi {r^3}$
For Example:Â If a radius of hemisphere is $5cm$, then
Volume of a hemisphere is ${2 \over 3}\pi \times {5^3} = 261.66c{m^3}$

(6) Volume of a spherical shell whose outer and inner radii are R and r respectively is given by
$V = {4 \over 3}\pi \left( {{R^3} - {r^3}} \right)$
For Example:Â If Internal radii $r = 5cm$ and external radii $R = 7cm$,then
$V = {4 \over 3}\pi \left( {{7^3} - {5^3}} \right) = 912.69c{m^3}$