Question
Sphere 1 (Area = A = 4 r 2 , Volume = V = (4/3) r 3 ) has a radius of r 1 ,
Sphere 1 (Area = A = 4 r2, Volume = V = (4/3) r3) has a radius of r1, and sphere 2 has a radius of r2 = 2 * r1.(Hint: Watch Session 13/Lecture/Video Lessons on Matter/Area, Volume, and Scaling Lesson)
3 - What is the ratio of the area of sphere 1 to sphere 2 (i.e., A1/A2)?
4 - What is the ratio of the volume of sphere 1 to sphere 2 (i.e., V1/V2)?
5 - Which grows faster with increasing radius, the volume of a sphere or the area of a sphere?
6 - What is the ratio of the volume of a sphere to the area of a sphere (i.e. V/A) in terms of constants and r, the radius of the sphere?
7 - In general, for any shape, given that A ~ r2 and V ~ r3, which grows faster with an increase in dimensions, area or volume?
New Problem
8 - Given their relative surface-area-to-volume ratios, at the same temperature, which can radiate its heat from its surface faster, a large object or a small object? (Hint: Watch Session 13/Lecture/Video Lessons on Matter/Heating and Cooling Lesson)
New problem
9 - Which cools a drink faster, crushed ice of a given mass m, or larger cubed ice of the same given mass m, and why? (Hint: Watch Session 13/Lecture/Video Lessons on Matter/Heating and Cooling Lesson)
A scale model of an object (m = 10 kg, A = 35 cm2, V = 40 cm3) is made such that the dimensions of the scale model are 5 times larger than the original object, but the scale model is identical to the object in every other way. Answer the following questions: (Hint: Watch Session 13/Lecture/Video Lessons on Matter/Area, Volume, and Scaling Lesson)
10 - What is the mass mmodel(in kg)of the scale model?
11- What is the surface area Amodel(in cubic cm) of the scale model?
12 - What is the volume Vmodel(in cubic cm) of the scale model?
A scale model of an object (m = 10 kg, A = 35 cm2, V = 40 cm3) is made such that the dimensions of the scale model are 5 times smaller than the original object, but the scale model is identical to the object in every other way. Answer the following questions: (Hint: Watch Session 13/Lecture/Video Lessons on Matter/Area, Volume, and Scaling Lesson)
13 - What is the mass mmodel(in kg) of the scale model?
14 - What is the surface area Amodel(in cubic cm) of the scale model?
15 - What is the volume Vmodel(in cubic cm) of the scale model?
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College Physics A Strategic Approach Volume 1
Authors: Randall D. Knight, Brian Jones, Stuart Field
2nd Edition
0321602285, 978-0321602282
