Physics quiz question: volume of Lake Nacimiento

Physics 205A Quiz 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

The California Department of Water Resources reported[*] that Lake Nacimiento had 336,643 acre-feet of water in April 2017. An acre is defined as the area of a 66 ft × 660 ft plot of land, and an acre-foot is defined as the volume of an acre of land covered by one foot of water. This amount of water in cubic feet is:
(A) 0.129396 ft³.
(B) 7.72826 ft³.
(C) 1.46642×10¹⁰ ft³.
(D) 9.67835×10¹⁰ ft³.

[*] cdec.water.ca.gov/cgi-progs/queryMonthly?NCM.

Correct answer (highlight to unhide): (C)

The volume of Lake Nacimiento can be determined from converting the units from the given value of 336,643 acre-feet by setting up conversion factors such that unwanted units cancel (acres) while desired units remain (feet):

volume of "336,643 acre-ft" = (336,643 acres)·(1 ft),

336,643 acre-ft = (336,643 acres)·(1 ft)·((66 ft × 660 ft)/(1 acre)),

336,643 acre-ft = 14,664,169,080 ft²,

or to six significant figures, the volume of Lake Nacimiento is 1.46642×10¹⁰ ft³.

(Response (A) is (66 × 660)/(336,643); response (B) is (336,643)/(66 × 660); response (D) is (336,643)·(66³).)

Sections 70854, 70855
Exam code: quiz01D4mP
(A) : 6 students
(B) : 13 students
(C) : 41 students
(D) : 2 students

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.21