Question

The volume of a sphere is given by V = 4πr3/3, where r is the radius. Use MATLAB to compute the radius of a sphere having a volume 40 percent greater than that of a sphere of radius 4 ft.

Answer 1

Calculate the volume of the sphere as follows:

V = 4/3 πr3

 

Here, r is the radius of the sphere.

 

Substitute 4 ft for r.

V = 4/3 π(4)3

= 256π/3 ft3

 

Calculate the new radius of the sphere (R), when volume of sphere increased by 40% as follows:

Vnew = V + 40% of V

 

Substitute (256π/3)ft3 for V and 4/3 πR3 for Vnew

 

4/3πR3 = (256π/3) + 40%(256π/3)

4/3πR3 = (256π/3) + (40/100)(256π/3)

R = 3√64 + 0.4 × 64

R = 4.4748 ft

 

Calculate the R using the following MATLAB commands as follows:

>> r=4;

>> V=4/3*pi*r^3;

>> V1=40/100*V+V;

>> syms R

>> solve(4/3*pi*R^3-V1)

ans =

[4.474755768]

 

Thus, the required radius is 4.4748 ft.

Thus, the required radius is 4.4748 ft.