Question

A spherical glass vessel has a cylindrical neck 8 cm long, 2cm 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 345 cm³. Check whether she is correct, taking the above as the inside measurements, and π = 3.14

Answer 1

Height (h) of cylindrical part = 8 cm

Radius (r₂) of cylindrical part = `2/2` = 1 cm

Radius (r₁) spherical part = `8.5/2` = 4.25 cm

Volume of vessel = Volume of sphere + Volume of cylinder

= `4/3pir_1^3+pir_2^2h`

= `4/3pi(8.5/2)^3 +pi(1)^2(8)`

= `4/3xx3.14xx76.765625 + 8 xx 3.14`

= 321.392 + 25.12

= 3346.512

= 346.51 cm³

Hence, she is wrong.