§14.4b STp786: P3.
Problem 3 :
“Assume the conical container
and the cylindrical tub of popcorn
are full and they hold the same
amount of popcorn” . . . means
their volumes are =.
π r 2h
VCone =
3
VCyl = π r 2 h
169.56 in
3
169.56 in 3
“Assume the conical container
and the cylindrical tub of popcorn
are full and they hold the same
amount of popcorn” . . . means
their volumes are =.
π r 2h
VCone =
3
VCyl = π r 2 h
π r 2h
Vcone =
3
3.14 • r 2 h
169.56 ≈
3
3 •169.56 3 • 3.14 • r 2 h
≈
3.14
3 • 3.14
162 ≈ r 2 h
If 162 ≈ r 2 h, then possible r and h
combinations include:
1) r = 9 , h = 2
2) r = 10 , h = 1.62
and
3) r = 6 →162 = 36 • h
→
162
= h = 4.5
36
169.56 in
3
169.56 in 3
“Assume the conical container
and the cylindrical tub of popcorn
are full and they hold the same
amount of popcorn” . . . means
their volumes are =.
π r 2h
VCone =
3
VCyl = π r 2 h
3in
3in
Vcyl = Vcone
π r 2h
169.56 =
3
3
3.14 • 32 • h 3.14 • 9 • h
169.56 ≈
≈
3
1 3
169.56 ≈ 3.14 • 3 • h
169.56
3.14 • 3 • h
≈
3.14 • 3
3.14 • 3
h ≈ 18in