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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
Solution
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.
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