jlooman2002
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What is the volume of the item described? An ice cream cone with a cone of radius 2 cm and height of 9 cm with a hemisphere of ice cream on top of radius 2 cm. Select the exact answer in terms of ​ π ​ and the approximate answer rounded to the nearest whole number

Respuesta :

scme1702
Volume of hemisphere = 2πr³/3
Volume of cone = πr²h/3

Where r = 2 and h = 9

Volume = volume of hemisphere + volume of cone
Volume = 2π(2)³/3 + π(2)²(9)/3
Volume = 16π/3 + 36π/3
Volume = 52π/3

Answer:

The volume of item is [tex]\frac{52}{3}\pi[/tex].

Step-by-step explanation:

The volume of cone

[tex]V_1=\frac{1}{3}\pi r^2h[/tex]

Where r is radius of cone and h is the height of cone.

It is given that the radius of cone is 2 cm and the height of cone is 9 cm. So, the volume of cone is

[tex]V_1=\frac{1}{3}\pi (2)^2(9)=12\pi[/tex]

The volume of hemisphere

[tex]V_2=\frac{2}{3}\pi r^3[/tex]

Where r is radius of hemisphere.

It is given that the radius of hemisphere is 2 cm. So, the volume of hemisphere is

[tex]V_2=\frac{2}{3}\pi (2)^3=\frac{16}{3}\pi[/tex]

The volume of ice cream is

[tex]V=V_1+V_2[/tex]

[tex]V=12\pi+\frac{16}{3}\pi[/tex]

[tex]V=\frac{36+16}{3}\pi[/tex]

[tex]V=\frac{52}{3}\pi[/tex]

Therefore the volume of item is [tex]\frac{52}{3}\pi[/tex].

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