a hemispherical tank is made up of an iron sheet 1cm thick .if the inner radius is 1m ,then find the volume of the iron used to make the tank .
Answers
Given the Inner Radius of the Hemispherical tank as : 1m
It is also mentioned that the Thickness of Iron sheet is 1cm
⇒ The Outer Radius of the Hemispherical tank will be Sum of Inner Radius and Thickness of Iron sheet
⇒ The Outer Radius of the Hemispherical Tank : 1m + 1cm = 1m + 0.01m
⇒ The Outer Radius of the Hemispherical Tank = 1.01m
Inorder to Calculate the Volume of Iron used, 1st we need to calculate the Volumes of both Inner Hemisphere and Outer Hemisphere.
We know that Volume of a Sphere is : 4/3 × π × r³
⇒ Volume of Hemisphere will be Half of the Volume of sphere
⇒ Volume of Hemisphere = 2/3 × π × r³
⇒ Volume of the Inner Hemisphere = 2/3 × π × 1³
⇒ Volume of the Outer Hemisphere = 2/3 × π × (1.01)³
If we Imagine the Hemispherical tank : We can Notice that Volume of Iron used will be the Difference of Volume of the Outer Hemisphere and the Volume of Inner Hemisphere.
⇒ Volume of Iron used = 2/3 × π × (1.01)³ - 2/3 × π
⇒ Volume of Iron used = 2/3 × π × ((1.01)³ - 1) = 2/3 × π × (1.030301 - 1)
⇒ Volume of Iron used = 2/3 × 22/7 × 0.030301 = 0.06346 m³
⇒ Answer :- 0.063487 cm^3
⇒ Given :-
Inner radius = 1 m
Iron sheet is 1 cm Thick
⇒ Solution :-
Let outer radius be R = Inner radius + thickness of iron sheet
= 101 cm
Inner radius be r = 1m = 100 cm
∴ Volume of the iron = (⅔)×(22/7)× (R^3-r^3)
(2/3)×(22/7)×(101^3-100^3)
44/21×30301 cm^3
63487.80952 cm^3
0.063487 cm^3