The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Fig. 12.7 is (πr²/3)[3h - 2r]. Is the following statement true or false and justify your answer
Solution:
Given a cylindrical vessel with a hemispherical portion.
We have to determine if the capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom is (πr²/3)[3h - 2r]
Capacity of the given vessel = capacity of cylinder - capacity of hemisphere
Volume of cylinder = πr²h
Volume of hemisphere = (2/3)πr³
Capacity of the vessel = πr²h - (2/3)πr³
= πr²/3 (3h - 2r) cubic units
Therefore, the capacity of the vessel is πr²/3 (3h - 2r) cubic units.
✦ Try This: A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 m and the diameter of the hemisphere is 3.5 m. Calculate the volume of the vessel.
Given, a hollow cylinder is fitted with a hemispherical bottom of the same base.
The depth of the cylinder, h = 14/3 m
The diameter of the hemisphere = 3.5 m
Radius, r = 3.5/2 m
We have to calculate the volume of the vessel.
Volume of the vessel = volume of cylinder + volume of hemisphere.
Volume of cylinder = πr²h
Volume of hemisphere = (2/3)πr³
Volume of the vessel = πr²h + (2/3)πr³
= πr²(h + 2r/3)
= (22/7)(3.5/2)²(14/3 + 2(3.5/2)/3)
= (22/7)(3.5/2)²[(14 + 3.5)/3]
= (22)(3.5/2)(0.5/2)(17.5/3)
= 56.15 m³
Therefore, the volume of the vessel is 56.15 m³
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13
NCERT Exemplar Class 10 Maths Exercise 12.2 Problem 6
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Fig. 12.7 is (πr²/3)[3h - 2r]. Is the following statement true or false and justify your answer
Summary:
The statement “The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Fig. 12.7 is (πr²/3)[3h - 2r]” is true
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