Question

find the maximum volume of a cone that can be carved be out of a solid hemisphere of radius r​

Answer 1

Explanation:

Hello

Step-by-step explanation:

Solution:-

♥️ Radius of the base of cone=radius of sphere=r

Also

Height of the cone= radius of the hemisphere

Therefore

Volume of the cone=

$= \frac{1}{3} \pi {r}^{2} \times r$

$= \frac{1}{3} \pi {r}^{3}$

Answer 2

Answer:

Let the radius of the hemisphere = r units

Radius of the cone = radius of the hemisphere

height of the cone = radius of the hemisphere

h = r ----( 1 )

Therefore ,

Required

maximum volume of the cone = ( 1/3 ) πr²h

V = ( 1/3 ) × π × r² × r

= ( 1/3 ) × πr³ cubic units

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