Question

a hemispherical dome of a building contains 56 4/7 m³ of air. Find the radius of the dome

Answer 1

Hope you like my process
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Hemispherical Dome :
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Semi - sphere monument of large size
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Formula to be used:-
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=> Volume of sphere = (4/3) π r³

=> Volume of Hemisphere

= Volume of sphere ÷ 2

= ⅔ π r³

where ,

r = radius of sphere

π = 22/7

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Given
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=> Volume of air in dome = 56 ⁴/7 m³

By problem
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=> ⅔ π r³ = 56 ⁴/7

=> ⅔ × 22/7 × r³ = 564/7

$= > {r}^{3} = 56 \frac{4}{7} \times \frac{7}{22} \times \frac{3}{2} \\ \\ = > {r}^{3} = \frac{396}{7} \times \frac{7}{22} \times \frac{3}{2} = 27 \\ \\ = > r = \sqrt[3]{ {3}^{3} } = 3$

Thus the required radius of dome = 3 m

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Hope this is your required answer

Proud to help you

Answer 2

Answer:

Let r be the radius of the hemispherical dome

now,volume of the hemispherical dome=56 4/7m^3

Step-by-step explanation:

==>2/3 pie R ^3=396/7

==>2/3 ×22/7r^3==>396/7

==> 44/3r^3==396

==> r^3=396×3/44

==>r^3 =27

==> r=3

So, radius is 3 m..

hope it will help u..