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hemisphere fits snugly inside a cylinder with a radius of 6 cm. A cone fits snugly inside the same hemisphere.

What is the volume of the cylinder?
π cm3
What is the volume of the cone?
π cm3
Estimate the volume of the hemisphere by calculating the average of the volumes of the cylinder and cone.
π cm3

Sagot :

oladayoademosu

a. The volume of the cylinder is 216π cm³  

b. The volume of the cone is 72π cm³

c. The volume of the hemisphere is 144π cm³

 

a. Volume of the cylinder

The volume of the cylinder is 216π cm³  

Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

So, the volume of the cylinder V = πr²h where

  • r = radius of cylinder = 6 cm and
  • h = height of cylinder = radius of hemisphere = 6 cm

So, V = πr²h

= πr² × r

= πr³

= π(6 cm)³

= 216π cm³

So, the volume of the cylinder is 216π cm³  

b. Volume of the cone

The volume of the cone is 72π cm³  

Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.

So, the volume of the cone V' = πr²h/3 where

  • r = radius of cone = 6 cm and
  • h = height of cone = radius of hemisphere = 6 cm

So, V' = πr²h/3

= πr² × r/3

= πr³/3

= π(6 cm)³/3

= 216π/3 cm³

= 72π cm³

So, the volume of the cone is 72π cm³  

c. Volume of hemisphere

The volume of the hemisphere is 144π cm³  

Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'

So, V" = (V + V')/2

V" = (216π cm³ + 72π cm³)/2

V" = 288π cm³/2

V" = 144π cm³  

So, the volume of the hemisphere is 144π cm³  

Learn more about volume here:

https://brainly.com/question/25248189

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