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Maths-

General

Easy

Question

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m , then find the volume of the iron used to make the tank ?

hint Hint:

The volume of hemisphere is $2 over 3 pi r cubed$ .

The correct answer is: 0.06348m3

Explanation:

We have given a hemisphere with thickness 1cm.

We have to find the volume of iron used to make the tank.

Step 1 of 1:
Since the hemispherical tank is made of 1cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.
The Volume of hemisphere of base radius r is equal to $2 over 3 pi r cubed$
The inner radius of the tank r = 1m
Thickness of iron = 1cm = 1/100 m =0.01m
Outer radius of the tank, R = 1m + 0.01m = 1.01m
The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.
Volume of the iron used to make the tank $2 over 3 pi R cubed minus 2 over 3 pi r cubed$
$equals 2 divided by 3 pi open parentheses R cubed minus r squared close parentheses$
$equals 2 divided by 3 cross times 22 divided by 7 cross times open square brackets left parenthesis 1.01 m right parenthesis cubed minus left parenthesis 1 m right parenthesis cubed close square brackets$
$equals 2 divided by 3 cross times 22 divided by 7 cross times open square brackets 1.030301 m cubed minus 1 m cubed close square brackets$
$equals 2 divided by 3 cross times 22 divided by 7 cross times 0.030301 straight m cubed$
$equals 0.06348 straight m cubed text (approx.) end text$
0.06348 m³of iron used to make the tank

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