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.

Explanation:

Given That:

radius of spherical core r₁ = 4cm

radius of tubular r₂ = 0.5cm

length of tubular l = 8cm

Volume of spherical V₁

Volume of tabular V₂

F ∝ V

and

As  V₁ is greater than V₂

⇒ F₁ is greater than F₂

F is force

V is volume

This is the required answer

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

option number c is the right answer.