dezjuanday25
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An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:3. If the diameter of the cone is 2 inches and the height is 5 inches, approximately what is the volume of chocolate ice cream in the cone? (round to nearest tenth)

A) 1.6 in3
B) 2.1 in3
C) 3.1 in3
D) 5.2 in3

Please help 35 points if you get this correct real answers only

Respuesta :

Volume of the cone is ⅓πr²h where r= radius=1 in and h=5 in, so volume is 5π/3 cu in. Divide this into 5 equal parts, one part=π/3, so chocolate is 3 parts=π cu in=3.1 cu in = 3.1 cu in approx, answer C.
calculista

Answer:

Option C. [tex]3.1\ in^{3}[/tex]

Step-by-step explanation:

Step 1

Find the volume of ice cream

we know that

The volume of the cone is equal to

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

In this problem we have

[tex]r=2/2=1\ in[/tex] ----> the radius is half the diameter

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3}\pi (1^{2})(5)=5.2\ in^{3}[/tex]

Step 2

Find the volume of chocolate ice cream in the cone

Let

x------> volume of vanilla ice cream

y------> volume of chocolate ice cream

we know that

[tex]\frac{x}{y} =\frac{2}{3}[/tex]

[tex]x=\frac{2}{3}y[/tex] -------> equation A

[tex]x+y=5.2[/tex] -----> equation B

substitute equation A in equation B

[tex]\frac{2}{3}y+y=5.2[/tex]

[tex]\frac{5}{3}y=5.2[/tex]

[tex]y=5.2*3/5=3.1\ in^{3}[/tex]