Question

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. By measuring the amount of water it holds, a child finds its volume to be $345c{m}^3$ ^. Check whether she is correct, taking the above as the inside measurements, and $\pi =3.14$. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Diameter of Sphere = d = 8.5 cm

Radius of Sphere $=r=\frac{d}{2}=\frac{8.5}{2}=4.25cm$

Volume of Sphere
$=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.14\times (4.25{)}^3=321.392c{m}^3$

Diameter of Cylinder $=d_1=2cm$

Radius of Cylinder $=r_1=\frac{d_1}{2}=1cm$

Height of Cylinder $=h=8cm$

Volume of Cylinder
$=\pi .(r_1{)}^2.h=3.14\times (1{)}^2\times 8=25.12c{m}^3$

Volume of Water in the Vessel = Volume of Vessel

= Volume of Sphere + Volume of Cylinder

$=321.392+25.12=346.512c{m}^3$

It means ,she was not correct.