Two watermelons, \(A\) and \(B\) , are on sale. Watermelon \(A\) has a circumference of 6 inches; watermelon \(B\) , 5 inches. If the price of watermelon \(A\) is 1.5 times the price of watermelon \(B\) , which watermelon is a better buy?
(Assume that the two watermelons are spheres).
(A) A
(B) B
(C) Neither
(D) Both
(E) Impossible to determine
Source: GMAT Club Tests - hardest GMAT questions
Answer:To determine a better buy - we need to find out which watermelon is cheaper per kilo. Watermelon with C=60 has a volume of 224,694,718 (cu. cm's?) and the watermelon with C=50 has volume of 130,031,759. C=60 watermelon is 1.7 times the size of C=50 watermelon. Therefore C=60 is obviously the better buy.
My questions: How do we come up with these two volumes with the equation 4/3 pie r^3. Also, what circumference equation is used to determine r in the sphere? I thought the circumference can only be determined on a 2 dimensional object and not a 3 dimensional one (sphere). Thank you.
both are spherical. circumference is given => radius can be calculated => volume
ignore pi in both results. 1.5 * 20.85 = ~31-32
hence although you pay 1.5 times the price of B for A, you are getting bigger volume => less cost per unit weight.