Question

An ice cream cone has a height of 4 inches and a radius of 3 inches as shown. The ice cream completely fills the cone, as well as the half-sphere above the cone. What is the total volume of the ice cream and the cone?

Answer 1

Answer:

20 radius check the attachment for the answer

hope it helps you

Answer 2

Given:-

• Height of Cone = 4 inches

• Radius of base of Cone = 3 inches

To Find:-

• Total Volume of Ice Cream

• Total Volume of Cone

Formula used:-

• ${\boxed{\sf{Volume\:of\:Hemisphere = \dfrac{2}{3}\pi r^3}}}$

• ${\boxed{\sf{Volume\:of\:Cone = \dfrac{1}{3}\pi r^2h}}}$

Solution:-

Firstly,

$\sf :\implies\:Volume\:of\:Cone = \dfrac{1}{3}\pi r^2h$

Here,

• r = 3 inches

• h = 4 inches

Putting values,

$\sf :\implies\:Volume\:of\:Cone = \dfrac{1}{3}\times\dfrac{22}{7}\times 3^2\times4$

$\sf :\implies\:Volume\:of\:Cone = \dfrac{22\times36}{21}$

$\sf :\implies\:Volume\:of\:Cone = \dfrac{792}{21}inches^3$

Hence, The Volume of Cone is 792/21 inches³.

Now,

Volume of Ice Cream = Volume of Cone + Volume of Hemisphere

Volume of Ice Cream = $\dfrac{792}{21} + \dfrac{2}{3}\pi r^3$

Volume of Ice Cream = $\dfrac{792}{21} + \dfrac{2}{3}\times \dfrac{22}{7} \times3^3$

Volume of Ice Cream = $\dfrac{792}{21} +\dfrac{44\times27}{21}$

Volume of Ice Cream = $\dfrac{792}{21} + \dfrac{1188}{21}$

Volume of Ice Cream = $\dfrac{1188+792}{21}$

Volume of Ice Cream = $\dfrac{1980}{21}inches^3$

Hence, The Volume of Ice Cream is 1980/21 inches³.

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