Volume of material used in constructing a hollow cylinder of height 24 cm and thickness 1 cm is 96π. What is the sum of the internal and external radii?

height 24 cm and thickness 1 cm 

volume = 96π

let the outer radius be R and inner radius be r

Inner radius r = (R - 1) cm  (thickness = 1 cm, Inner radius = outer radius - thickness}

V = (Volume of the external cylinder) - (Volume of the Internal cylinder)

 $$V = π\times h\times (R^2 - r^2)$$   (i)

put the given values in eq. (i), we get

$$96π = π\times h\times [R^2 - (R-1)^2]$$

 $$4 = R^2- R^2 + 2R - 1$$

$$2R - 1 = 4$$

$$2R = 5$$

 R  = 2.5 cm

Inner radius, r = R - 1 = 2.5 - 1 = 1.5 cm

Thus,

 sum of the internal and external radii = R + r = 2.5 + 1.5 = 4 cm .