Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Tennis balls with a diameter of 2.5 in. are packaged 3 to a can. The can is a cylinder. Find the volume of the space in the can that is not occupied by tennis balls. Assume that the balls touch the sides, top, and bottom of the can. Round your answer to the nearest hundredth. What is the volume not occupied by balls?

Sagot :

Ryan2
a) First we calculate the volume of each ball:

[tex]\boxed{V=\frac{4\pi r^3}{3}}\\ \\ \boxed{V=\frac{4*(3,14)*(1.25)^3}{3}=8,177 \ square \ inch}[/tex]

b) Now we calculate the volume of tree balls:

[tex]\boxed{V_T=3*8,177=24.531 \ square \ inch}[/tex]

c) Now we calculate the volume of cylinder:

c1) Base area:

[tex]\boxed{A_b=\pi r^2}\\ \\ \boxed{A_b=3,14*(1,25)^2=4.906 \ square \ inch}[/tex]

c2) Cylinder height

[tex]\boxed{h=3*(2.5)=7.5 \ inch}[/tex]

c3) Cylinder Volume:

[tex]V_C=A_b*h\\ \\ \boxed{V_C=4.906*7.5=36.795 \ cubic \ inch}[/tex]

d) Finally we calculate the internal space:

[tex]\boxed{\boxed{s=36.795-24.531= 12,264\ cubic \ inch}}[/tex]
Lilith
[tex]d=2.5 \ in \\ \\ r=\frac{d}{2}=\frac{2.5}{2}=1.25 \ in \\ \\ \pi=3.14 \\ \\Volume \ of \ a \ Cylinder : \\ \\V = \pi r^2 h[/tex]

[tex]h=3\cdot d = 3*2.5 = 7.5 \ in \\ \\V_{c} = 3.14\cdot (1.25)^2\cdot 7.5 = 23.55 * 1.5625=36.80 \ in^3[/tex]


[tex]The \ volume \ of \ tree \ balls : \\ \\ V_{3b}= 3 \cdot \frac{4}{3} \pi r^3 = 4\pi r^3 \\ \\V_{3b}=4\cdot 3.14\cdot (1.25)^3= 12.56\cdot 1.9531 \approx 24.53 \ in^3 \\ \\V_{c}-V_{3b}=36.80-24.53 =12.27 \ in^3 \\ \\ Answer : \ The \ volume \ not \ occupied \ by \ balls \ it \ 12.27 \ in^3[/tex]



View image Lilith
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.