Cylinder

Scott Solomon

Cylinder = Three-Dimensional Shape with Circular Top and Base

Cylinder


Basics
r = radius = distance halfway across circular top or base
d = diameter = distance all the way across circular top or base
h = height
SA = Surface Area = area covering surface, including top and base, of cylinder
LA = Lateral Area = area covering surface, excluding top and base, of cylinder
V = Volume = space occupied by cylinder


Formulas (Mathematics Formula Sheet)
SA = 2πrh+ 2πr²
V = πr²h


Formulas (NOT on Mathematics Formula Sheet)
LA = 2πrh

r = \bf\displaystyle \frac{1}{2}d


Question
A can of soda has a radius of 3 inches and height 6 inches.  What is its surface area?

Answer
54π square inches

Answer Process
SA = 2πrh+ 2πr²
SA = 2 × π × 3 × 6+ 2 × π × 3² = 54π

Input Display Comment
clear blinker clears screen
2 × π × 3 × 6
+
2 × π × 3 square		 2*π*3*6+2*π*3² SA = 2πrh + 2πr²
enter 54π Answer
Cylinder


Question
With reference to the question above, what is the area of the can in decimal form?

Answer
169.6460033 square inches

Answer Process
See Toggle.
54π ⇔ 169.6460033

Input Display Comment
clear blinker clears screen
2 × π × 3 × 6
+
2 × π × 3 square		 2*π*3*6+2*π*3² SA = 2πrh + 2πr²
enter 54π
toggle 169.6460033 Answer
(Toggle)
Cylinder

Question
With reference to the question above, what is the area of the can to the nearest tenth?

Answer
169.6 square inches

Answer Process
See Rounding.
169.6460033 → 169.6


Question
A can of soda has a radius of 3 inches and height 6 inches.  To the nearest tenth of a square foot, what is its surface area?

Answer
1.2 square feet

Answer Process
See Measurement.
Square Feet = Square Inches ÷ 144 square inches per square foot
Square Feet = 169.6460033  ÷ 144 = 1.178097245 = 1.2 after rounding

Input Display Comment
clear blinker clears screen
2 × π × 3 × 6
+
2 × π × 3 square		 2*π*3*6+2*π*3² SA = 2πrh + 2πr²
enter 54π
toggle 169.6460033
169.6460033 ÷ 144 169.6460033÷144 Square Feet = Square Inches ÷ 144 square inches per square foot
enter 1.178097245 Answer
Cylinder


Question
A can of soda has a radius of 4 inches and height 8 inches.  To the nearest hundredth of a cubic inch, what is its volume?

Answer
402.12 cubic inches

Answer Process
V = πr²h
V = π × 4² × 8 = 128π = 402.1238597 after toggle = 402.12 after rounding

Input Display Comment
clear blinker clears screen
π × 4 square × 8 π*4²*8 V = πr²h
enter 128π
toggle 402.1238597 Answer
(before rounding)
Cylinder


Question
A can of soda has a diameter of \bf\displaystyle8\frac{1}{2} inches and height \bf\displaystyle9\frac{1}{4} inches.  To the nearest hundredth of a cubic inch, what is its volume?

Answer
524.89 cubic inches

Answer Process
r = \bf\displaystyle \frac{1}{2}d

r = \bf\displaystyle\frac{1}{2}\times8\frac{1}{2} = \bf\displaystyle\frac{17}{4}

V = πr²h

V = π x \bf\displaystyle\frac{17}{4}^{2}\times9\frac{1}{4} = \bf\displaystyle\frac{10693\pi }{64} = 524.8914101 after toggle = 524.89 after rounding

Input Display Comment
clear blinker clears screen
fraction 1 down 2 right
×
2nd mixed number 8 right 1 down 2 right		 \bf\displaystyle\frac{1}{2}*8\frac{1}{2} r = \bf\displaystyle \frac{1}{2}d
 enter \bf\displaystyle\frac{17}{4}  r
π × fraction 17 down 4 right square
×
2nd mixed number 9 right 1 down 4 right		 π*\bf\displaystyle\frac{17}{4}^{2}*9\frac{1}{4} V = πr²h
enter \bf\displaystyle\frac{10693\pi }{64}
toggle 524.8914101 Answer
(before rounding)
Cylinder


Question
A can of soda has a radius of 3 inches and height 6 inches.  To the nearest tenth of a square inch, what is its lateral area?

Answer
113.1 square inches

Answer Process
LA = 2πrh
LA = 2 x π x 3 x 6 = 36π = 113.0973355 after toggle = 113.1 after rounding

Input Display Comment
clear blinker clears screen
2 × π × 3 × 6 2*π*3*6 LA = 2πrh
enter 36π
toggle 113.0973355 Answer
(before rounding)
Cylinder


Practice – Questions
1.  A canister has a radius of 5 inches and height 7 inches.  To the nearest tenth of square inch, what is its surface area?

2.  With reference to Question 2, what is the canister’s surface area to the nearest tenth of a square foot?

3.  A canister has a radius of 5 inches and height 7 inches.  To the nearest hundredth of a cubic inch, what is its volume?

4.  A canister has a diameter of \bf\displaystyle10\frac{1}{2} inches and height \bf\displaystyle7\frac{1}{4} inches.  To the nearest hundredth of a cubic inch, what is its volume?

5.  A canister has a radius of 5 inches and height 7 inches.  To the nearest tenth of a square inch, what is its lateral area?


Practice – Answers
1.  377.0 square inches

2.  2.6 square feet

3.  549.78 cubic inches

4.  627.78 cubic inches

5.  219.9 square inches

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