) It would take times filling up glass B and pouring into glass A to fill up glass A. b) If the height of the glasses doubled, then the volumes would increase timesResponse area. (Hint: Use your formulas to substitute V=13πr2h and V=πr2h ) c) If the radius of the glasses doubled, then the volumes would increase timesResponse area. (Hint: Use your formulas to substitute V=13πr2h and V=πr2h ) d) If the radius and the height both doubled, then the volumes would increase timesResponse area. (Hint: Use your formulas to substitute V=13πr2h and V=πr2h )
b) If the height of the glasses doubled, then the volumes would increase by 2 times.
Let's use the formula V=πr^2h for both glasses:
For glass A: V_A = πr_A^2 * 2h_A
For glass B: V_B = πr_B^2 * 2h_B
Since the height doubles for both glasses, we can see that the volume for each glass will increase by 2 times.
c) If the radius of the glasses doubled, then the volumes would increase by 4 times.
Using the same formula as above, we have:
For glass A: V_A = π(2r_A)^2 * h_A = 4πr_A^2h_A
For glass B: V_B = π(2r_B)^2 * h_B = 4πr_B^2h_B
Therefore, when the radius doubles, the volume increases by 4 times.
d) If the radius and the height both doubled, then the volumes would increase by 8 times.
Using the same formula as above, we have:
For glass A: V_A = π(2r_A)^2 * 2h_A = 8πr_A^2h_A
For glass B: V_B = π(2r_B)^2 * 2h_B = 8πr_B^2h_B
Therefore, when both the radius and height double, the volume increases by 8 times.