Volume to height of triangular prisms or
height/radius of cylinders [CHALLENGE LEVEL]
Use 3.14 for .
EXAMPLE: (Base given)
EXAMPLE:
volume = 6800 cm3
area of triangular base = 170 cm2
volume = 226.08 in3
3 in.
What’s the height of the prism?
What’s the height of the cylinder?
V = Bh
6800 = 170 h
h = 6800/170 = 40 cm
V =  r2 h
226.08 = (3.14)(32)(h)
226.08 = (3.14)(9)(h)
226.08 = 28.26 h
h = 226.08/28.26 = 8 in.
EXAMPLE: (need to calculate Base)
EXAMPLE:
volume = 6800 cm3
What if instead we’d been given the volume
of a cylinder (226.08 in3) and the height
(8 in) and asked to find the radius?
17 cm
20 cm
What’s the height of the prism?
V =  r2 h
226.08 = (3.14)(r2)(8)
226.08 = 25.12 r2
r2 = 226.08/25.12
r2 = 9
r = √9 = 3 in.
Before we can find that, we need to get the
area of the prism’s base, a triangle.
B = ½ bh
B = ½ (17)(20) = 170 cm2
Now we can use the prism volume formula.
V = Bh
6800 = 170 h
h = 6800/170 = 40 cm
D. Stark 4/22/2016
1
1) volume = 24 in3
5) volume = 110.528 m3
4m
??? in
What’s the height?
What’s the height of the prism?
6) volume = 141.3 ft3
6 ft
2) A prism has a triangular base with the
area 12 ½ ft2. The prism has a volume of
100 ft3. What’s the height of the prism?
What’s the height?
3) A Toblerone chocolate bar box with a
volume of 58.464 cm3 is shown below. The
triangular Base (B) has a height of 2.4 cm
and a base (b) of 2.8 cm. What’s the height
of the prism?
7) A cylindrical canister can hold 169.56
cubic feet of water. If the height is 6 ft,
what’s the radius?
4) volume = 189 in3
8) A storage tank has a height of 12 ft and a
volume of 1356.48 ft3. What’s the diameter
of the tank?
What’s the area of the triangular Base of
the prism?
D. Stark 4/22/2016
2
Volume to height of triangular prisms or
height/radius of cylinders [CHALLENGE LEVEL] KEY
Use 3.14 for .
1) volume = 24 in3
5) volume = 110.528 m3
4m
??? in
What’s the height?
What’s the height of the prism?
First, find the triangular Base (B).
B = ½ (3)(4) = 6 in2
Then use the volume formula.
V = Bh
24 = 6 h
h = 24/6 = 4 in
V = Bh
100 = 12 ½ h
h = 100/12 ½ = 8 ft
6) volume = 141.3 ft3
6 ft
2) A prism has a triangular base with the
area 12 ½ ft2. The prism has a volume of
100 ft3. What’s the height of the prism?
V = r2h
110.528 = (3.14)(42)h
110.528 = (3.14)(16)h
110.528 = 50.24 h
h = 110.528/50.24
h = 2.2 m
What’s the height?
First divide the diameter by 2 to get the
radius, r = 3 ft.
Then use the volume formula.
V = r2h
141.3 = (3.14)(32)h
141.3 = (3.14)(9)h
141.3 = 28.26 h
h = 141.3 /28.26 = 5 ft
D. Stark 4/22/2016
3
3) A Toblerone chocolate bar box with a
volume of 58.464 cm3 is shown below. The
triangular Base (B) has a height of 2.4 cm
and a base (b) of 2.8 cm. What’s the height
of the prism?
7) A cylindrical canister can hold 169.56
cubic feet of water. If the height is 6 ft,
what’s the radius?
V = r2h
169.56 = (3.14)(r2)(6)
169.56 = 18.84 r2
r2 = 169.56/18.84
r2 = 9
r = √𝟗 = 3 ft
First, find the triangular Base (B).
B = ½ (2.8)(2.4) = 3.36 cm2
Then use the volume formula.
V = Bh
58.464 = 3.36 h
h = 58.464 /3.36 = 17.4 cm
4) volume = 189 in3
What’s the area of the triangular Base of
the prism?
Use the volume formula.
V = Bh
189 = B (21)
B = 189/21 = 9 in2
(This is the area of the triangular base,
so the units are square units.)
8) A storage tank has a height of 12 ft and a
volume of 1356.48 ft3. What’s the diameter
of the tank?
V = r2h
1356.48= (3.14)(r2)(12)
1356.48= 37.68 r2
r2 = 1356.48/37.68
r2 = 36
r = √𝟑𝟔 = 6 ft
Since the radius is 6ft, the diameter is
12 ft.
D. Stark 4/22/2016
4