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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,  we have
(i)  Surface area  = 4\pi{r^2}
For Example: 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: 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: 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: 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: 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: 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}



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