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 m_model(in kg)of the scale model?

11- What is the surface area A_model(in cubic cm) of the scale model?

12 - What is the volume V_model(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 m_model(in kg) of the scale model?

14 - What is the surface area A_model(in cubic cm) of the scale model?

15 - What is the volume V_model(in cubic cm) of the scale model?