Question

You have two balloons, one that has a spherical core of radius 4 cm and the other that is tubular with a radius of 0.5 cm and a length of 8 cm. Knowing that the force that you can initially apply to trying to expand each balloon is directly proportional to the volume of the balloon, show that the higher initial stress is achievable with the spherical balloon.

Answer 1

Step-by-step explanation:

Given That:

radius of spherical core r₁ = 4cm

radius of tubular r₂ = 0.5cm

length of tubular l = 8cm

Volume of spherical V₁

`=(4)/(3) \pi r_1^3`

`=(4)/(3) \pi(4)^3\\\\=(4)/(3) \pi 64\\\\=268.1cm^3`

Volume of tabular V₂

`=\pi r ^2_2h`

`=\pi(0.5)^2* 8\\\\ =\pi 90.250*8\\\\ =\pi 2\\\\=6.283cm^3`

F ∝ V

`F_1 \propto V_1` and
`F_2 \propto V_2`

As V₁ is greater than V₂

⇒ F₁ is greater than F₂

F is force

V is volume

This is the required answer