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