The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius holds pints, how many gallons will a similar can with a 24-inch radius hold?

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Answer 1 · 2018-07-30T02:33:59

#color(brown)(V_2 = 8 " gallons"#

#"Volume of cylinder " = V = pi r^2 h#

Let #r_1, h_1# be the radius and height of the first cylinder and #r_2, h_2# the second.

#color(purple)(r_1 = 6 " inch", r_2 = 24 " inch", V_1 = 1 " pint"#

#V_1 = pi r_1^2 h_1, V_2 = pi r_2 ^2 h_2#

#V_2 / V_1 = r_2 ^3 / r_1 ^3 = 24^3 / 6^3, " given"#

#1 gallon = 8 pints#

#:. V_2 = (24/6)^3 * V_1 = (24/6)^3 * 1 = 4^3 = 64 " pints"#

#color(brown)(V_2 = 64 / 8 = 8 " gallons, as 8 pints = 1 gallon"#