he water glasses are filled to the same height and have the same radius.
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(4 points)
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a) It would takeResponse area 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
.
9 answers
b) If the height of the glasses doubled, then the volumes would increase 2 times.
c) If the radius of the glasses doubled, then the volumes would increase 4 times.
d) If the radius and the height both doubled, then the volumes would increase 8 times.
a) It would take 2 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 4 times.
c) If the radius of the glasses doubled, then the volumes would increase 4 times.
d) If the radius and the height both doubled, then the volumes would increase 16 times.
a) It would take 3 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 4 times.
c) If the radius of the glasses doubled, then the volumes would increase 4 times.
d) If the radius and the height both doubled, then the volumes would increase 8 times.
a) It would take 2 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 4 times.
c) If the radius of the glasses doubled, then the volumes would increase 4 times.
d) If the radius and the height both doubled, then the volumes would increase 8 times.
and V=πr2h
a) The volume of glass A is V=1/3 * π * r^2 * h. Since glass B is filled up 3 times, the volume poured into glass A is 3 * V, which is 3 * (1/3 * π * r^2 * h) = π * r^2 * h. Therefore, it would take 3 times filling up glass B and pouring into glass A to fill up glass A.
b) If the height of the glasses doubled, the volume V' is 2 * V = 2 * (1/3 * π * r^2 * 2h) = 2/3 * π * r^2 * 2h = 4/3 * π * r^2 * h. So, the volumes would increase by 4/3 = 1.33 times.
c) If the radius of the glasses doubled, the volume V' is 4 * V = 4 * (1/3 * π * (2r)^2 * h) = 4/3 * π * (2r)^2 * h = 4 * π * r^2 * h. The volumes would increase by 4 times.
d) If the radius and the height both doubled, the volume V' is 8 * V = 8 * (1/3 * π * (2r)^2 * 2h) = 8/3 * π * (2r)^2 * 2h = 8 * π * r^2 * 2h. The volumes would increase by 8 times.