Answer:
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
- Choose any four numbers that are less than 10 for the height.
- Then, substitute into the formula and isolate "r". 10 = πr²h
- Double "r" to find the diameter.
- The area of the base is found (bolded) while you solve πr².
*I will use the calculator button for pi (π)
<u>Cylinder A: </u><u>h = 1</u>
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.
<u>Cylinder B: </u><u>h = 2</u>
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.
<u>Cylinder C: </u><u>h = 4</u>
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.
<u>Cylinder D: </u><u>h = 5</u>
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
- Choose a random number for volume that divides easily by 25.
- Substitute "V" and "r²" (r² = 25).
- Isolate "h".
- The area of the base is 78.54 cm² every time (A = πr²).
<u>Cylinder A: </u><u>V = 100</u>
100 = π25h
4 = πh
h = 1.27 The height is 1.27m.
<u>Cylinder B: </u><u>V = 200</u>
200 = π25h
8 = πh
h = 2.55 The height is 2.55m.
<u>Cylinder C: </u><u>V = 75</u>
75 = π25h
3 = πh
h = 0.95 The height is 0.95m.
<u>Cylinder D: </u><u>V = 125</u>
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.
