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A
A cylinder has a volume of 10 m' What might its dimensions be (height, area of base, radius, and
diameter)? Give 4 possible cylinders.
Volume 10 m
Height
Area of Base
Radius
Diameter
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?
How many possibilities are there? Why do you think so?
B. A cylinder has a diameter of 10 cm. What might its volume be? Give the radius, area of base and
height for 4 possible volumes
Diameter 10 cm
Radius
Area of Base
Height
Volume
Cylinder A
Cylinder B
Cylinder
Cylinder D
How do you know your answers are reasonable?

See below.

Step-by-step explanation:

PROBLEM A

The formula for the volume of a cylinder is

V = πr²h, where πr² is the area of the base.

V = area of base x height

*I will use the calculator button for pi (π)

Cylinder A: h = 1

10 = πr²h

10 = πr²(1)

10 = πr²                       Area of the base is 10m².

r = √ (10/π)

r = 1.78                        Radius is 1.78m.

d = 2r = 1.78*2 = 3.56                     Diameter is 3.56m.

Cylinder B: h = 2

10 = πr²h

10 = πr²(2)

5 = πr²                       Area of the base is 5m².

r = √ (5/π)

r = 1.26                      Radius is 1.26m.

d = 2r = 1.26*2 = 2.52                     Diameter is 2.52m.

Cylinder C: h = 4

10 = πr²h

10 = πr²(4)

2.5 = πr²                       Area of the base is 2.5m².

r = √ (2.5/π)

r = 0.89                        Radius is 0.89m.

d = 2r = 0.89*2 = 1.78                     Diameter is 1.78m.

Cylinder D: h = 5

10 = πr²h

10 = πr²(5)

2 = πr²                       Area of the base is 2m².

r = √ (2/π)

r = 0.80                     Radius is 0.8m.

d = 2r = 0.80*2 = 1.6                     Diameter is 1.6m.

The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.

There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.

PROBLEM B

Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.

We need the radius, which is half the diameter. r = d/2 = 10/2 = 5

Cylinder A: V = 100

100 = π25h

4 = πh

h = 1.27                      The height is 1.27m.

Cylinder B: V = 200

200 = π25h

8 = πh

h = 2.55                      The height is 2.55m.

Cylinder C: V = 75

75 = π25h

3 = πh

h = 0.95                      The height is 0.95m.

Cylinder D: V = 125

125 = π25h

5 = πh

h = 1.59                      The height is 1.59m.

The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.