Question

volume and surface area of a solid hemisphere are numerically equal . What is the diameter of hemisphere​

Answer 1

✬ Diameter = 9 ✬

Step-by-step explanation:

Given:

• Volume of a solid hemisphere is equal to the surface area of hemisphere.

To Find:

• What is the diameter of hemisphere ?

Solution: Let the diameter of hemisphere be d.

As we know that

➼ Volume of hemisphere = 2/3πr³

➼ Surface area of hemisphere = 3πr²

Let volume be equation (1) and surface area be equation (2)

A/q

• Equation 1 = Equation 2

$\implies{\rm }$ 2/3πr³ = 3πr²

$\implies{\rm }$ 2/3π (r)(r)(r) = 3π(r)(r)

$\implies{\rm }$ 2/3r = 3 (πr²/πr²)

$\implies{\rm }$ 2/3r = 3

$\implies{\rm }$ r = 3(3/2)

$\implies{\rm }$ r = 9/2

$\implies{\rm }$ r = 4.5

So, Diameter of hemisphere will be

➮ Diameter = 2(Radius)

➮ Diameter = 2(4.5)

➮ d = 9

Hence, Diameter of hemisphere will be 9.

Answer 2

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TO FIND :-

DIAMETER OF HEMISPHERE

SOLUTION:-

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Volume (Hemisphere)= $\frac{2}{3}$πr³

Surface area=3πr ²

∴3πr2 = $\frac{2}{3}$πr³

⇒r= $\frac{9}{2}$

⇒2r=9

⇒d=9.