# Math

A jar of peanut butter which is 3 inches in diameter and 4 inches high sells for \$0.60. At the same rate, what would be the price for a jar that is 6 inches in diameter and 6 inches high?

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1. V = ( d ^ 2 * pi / 4 ) * h

V1 = ( 3 ^ 2 * pi / 4 ) * 4 = ( 9 * pi / 4 ) * 4 = 36 * pi / 4

V2 = ( 6 ^ 2 * pi / 4 ) * 6 = ( 36 * pi / 4 ) * 6 = 216 pi / 4

V2 / V1 = ( 216 * pi / 4 ) / ( 36 * pi / 4 ) = 216 / 36 = 6

6 * 0.6 \$ = 3.6 \$

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2. volume = π(1.5)^2 (4)
= 9π cubic inches

volume of new jar π(3^2)(6) = 54π cubic inches
which is 6 times the original
So the new one should cost 6(.60) or \$3.00

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3. oops , typo

6 x 60cents = \$3.60

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4. Thanks Reiny and Bosian!!!

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5. OR

V = ( d ^ 2 * pi / 4 ) * h

V1 = ( 3 ^ 2 * pi / 4 ) * 4 = ( 9 * pi / 4 ) * 4 = 9 pi in ^ 3

V2 = ( 6 ^ 2 * pi / 4 ) * 6 = ( 36 * pi / 4 ) * 6 = 216 pi / 4 = 54 pi in ^ 3

V2 / V1 = 54 pi / 9 pi = 54 / 9 = 6

6 * 0.6 \$ = 3.6 \$

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