Question

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter o the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and $\pi = 3.14.$

Answer 1

Height (h) of cylindrical part = 8 cm
Radius (r2) of cylindrical part = 1 cm
Radius (r1) spherical part = 4.25 cm
Volume of vessel = Volume of sphere + Volume of cylinder
$=\frac{4}{3}\pi r^3_1+\pi r_2^2h$

$=\frac{4}{3}\pi(8.52)^3+\pi(1)^2(8)$

$=\frac{4}{3}×3.14×76.765625+8×3.14$
$=321.392+25.12$
$=346.51\ \text{cm}^3$
Hence, she is wrong.