Ice Cream: An ice-cream cone has a radius of 2.6 cm and a height of 6.8 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Ice Cream An icecream cone has a radius of 26 cm and a height of 68 cm The cone is filled with icecream and one additional scoop in the shape of a sphere with t class=

Respuesta :

Given:

Radius of cone is 2.6 cm and height is 6.8 cm.

The volume of cone is given as,

[tex]\begin{gathered} V_C=\pi\times r^2\times\frac{h}{3} \\ V_C=\pi\times(2.6)^2\times\frac{6.8}{3} \\ V_C=\frac{45.968\pi}{3} \end{gathered}[/tex]

Also, the radius of sphere is 2.,6 cm

[tex]\begin{gathered} V_S=\frac{4}{3}\times\pi\times r^3 \\ V_S=\frac{4}{3}\times\pi\times(2.6)^3 \\ V_S=\frac{70.304\pi}{3} \end{gathered}[/tex]

The total volume is,

[tex]\begin{gathered} V=V_C+V_S \\ V=\frac{45.968\pi}{3}+\frac{70.304\pi}{3} \\ V=\frac{116.272\pi}{3} \\ V=121.760\text{ cubic cm} \end{gathered}[/tex]

Answer: There are 121.760 cubic cm of ice cream.