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 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14
Solution:
A figure is drawn below to visualize the glass vessel.
As the glass vessel is a combination of a sphere and a cylinder
Volume of the glass vessel = volume of the spherical part + volume of the cylindrical part
Height of cylindrical part, h = 8 cm
Radius of cylindrical part, r₁ = 2/2 cm = 1 cm
Radius of spherical part, r₂ = 8.5/2 cm = 4.25 cm
Volume of the glass vessel = volume of the spherical part + volume of the cylindrical part
= 4/3 πr₂3 + πr₁2h
= π [(4/3) r₂3 + r₁2h]
= = 3.14 × [4/3 × 4.25 cm × 4.25 cm × 4.25 cm + 1 cm × 1 cm × 8 cm]
= 3.14 × (102.354 cm3 + 8 cm3)
= 3.14 × 110.354 cm3
= 346.51 cm3
Therefore, the child is approximately right while saying that the volume of the glass vessel is 345 cm3 which is nearly equal to the actual volume of the glass 346.51 cm3.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
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 345 cm³. Check whether she is correct, taking the above as the inside measurements, and π = 3.14.
NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.2 Question 8
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 345 cm3. The child is approximately correct while saying that the volume of the glass vessel is 345 cm3 which is nearly equal to the actual volume 346.51 cm3.
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