Question

A cylindrical tennis ball container contains three balls stacked on one another, such that they touch thewall of the container. The top and bottom balls also touch the lid and the base of thecontainer respectively. 

If the volume of a tennis ball is 160 cm3, then what is the volume of the container?

Answer 1

volume of the container is 1440√(105/11) cm³

Answer 2

The volume of the container is 715.30 cm³.

Step-by-step explanation:

The volume of a tennis ball is 160 cm³.

The volume of the sphere is $V_s=\frac{4}{3}\pi r^3$

$160=\frac{4}{3}\time \frac{22}{7}\times r^3$

$r^3=\frac{160\times 3\times 7}{4\times 22}$

$r^3=\frac{420}{11}$

$r=\sqrt[3]{\frac{420}{11}}$

$r=3.36$

The radius of the tennis ball is 3.36 cm.

The diameter of the tennis ball is $d=2r=2(3.36)=6.72\ cm$

A cylindrical tennis ball container contains three balls stacked on one another, such that they touch the wall of the container. The top and bottom balls also touch the lid and the base of the container respectively.

So, the height of cylinder = 3 times the diameter

i.e. $h=3\times 6.72$

$h=20.16\ cm$

Radius of cylinder = Radius of ball

Volume of the cylinder is given by,

$V=\pi r^2 h$

$V=\frac{22}{7}\times (3.36)^2\times 20.16$

$V=715.30\ cm^3$

Therefore, the volume of the container is 715.30 cm³.

#Learn more

If the lateral surface area of a cylinder is 94.2cm2, and its raius is 3cm then find: i the height ii its volume (use pie as=3.14)

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