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A spherical glass vessel has a cylindrical neck $8$ cm long, $2$ cm in diameter; the diameter of the spherical part is $8.5$ cm. Find the amount of water it can hold, when it is full up to the top. Also, find its external curved surface area. [Use $\pi = 3.14$]
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Radius of cylindrical neck = $1$ cm
Radius of spherical part = $\frac{8.5}{2}$ or $\frac{85}{20}$ cm
Amount of water hold by vessel = Volume of spherical part + Volume of cylindrical part
$= \frac{4}{3} \times 3.14 \times (\frac{85}{20})^3 + 3.14 \times (1)^2 \times 8$
$= 346.51$ cm$^3$ approx.
External CSA = CSA of spherical part + CSA of cylindrical part
$= 4 \times 3.14 \times (\frac{85}{20})^2 + 2 \times 3.14 \times 1 \times 8$
$= 277.11$ cm$^2$ approx.
Radius of spherical part = $\frac{8.5}{2}$ or $\frac{85}{20}$ cm
Amount of water hold by vessel = Volume of spherical part + Volume of cylindrical part
$= \frac{4}{3} \times 3.14 \times (\frac{85}{20})^3 + 3.14 \times (1)^2 \times 8$
$= 346.51$ cm$^3$ approx.
External CSA = CSA of spherical part + CSA of cylindrical part
$= 4 \times 3.14 \times (\frac{85}{20})^2 + 2 \times 3.14 \times 1 \times 8$
$= 277.11$ cm$^2$ approx.