Volume and surface area of a solid hemisphere are numerically equal. what is the diameter of hemisphere?

Question

Answer

Given that-
volume of hemisphere= surface area of hemisphere
2/3Πr^3=3Πr^2
r=9/2
so,diameter of hemisphere=2×9/2
=9

Answer

Volume of hemisphere=surface area of hemisphere2/3 pie r³=3 pie r²⇒2/3 r   =3 ⇒ r        =9/2 so, diameter = 2 radius      diameter=2*9/2      diameter=9

Answer

Volume of hemisphere = surface area of hemisphere2/3 πr³ = 3πr³=>  2r= 9=> r = 9/2diameter = 2r = 2×9/2 =9

Answer

Problem:

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

Solution:

Let's assume the diameter of the hemisphere to be 'd'.

Volume of Hemisphere:
The volume of a hemisphere is given by the formula: V = (2/3)πr³, where 'r' is the radius of the hemisphere.

We know that the radius of the hemisphere is half of the diameter, so r = d/2.

Substituting the value of radius in the volume formula:
V = (2/3)π(d/2)³
V = (2/3)π(d³/8)
V = (πd³)/12

Surface Area of Hemisphere:
The surface area of a hemisphere is given by the formula: A = 2πr² + πr², where 'r' is the radius of the hemisphere.

Again, substituting the value of radius:
A = 2π(d/2)² + π(d/2)²
A = 2π(d²/4) + π(d²/4)
A = π(d²/2) + π(d²/4)
A = (3πd²)/4

Equating Volume and Surface Area:
Since the volume and surface area are numerically equal, we can equate the equations:
(πd³)/12 = (3πd²)/4

To simplify the equation, we can multiply both sides by 12 to eliminate the fraction:
πd³ = 36πd²

Cancelling out π from both sides:
d³ = 36d²

Dividing both sides by d²:
d = 36

Conclusion:
The diameter of the hemisphere is 36 units.

Answer

2/3πr×r×r=3πr×rI.e. 2r=9I.e. r=9/2 after that u can..

Answer

Thanks pls give me solution

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