## Cylinder

Cylinder = Three-Dimensional Shape with Circular Top and Base 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 (provided by Mathematics Formula Sheet)

SA = 2πrh+ 2πr²

V = πr²h

Formulas (NOT provided by Mathematics Formula Sheet)

LA = 2πrh $\bf\displaystyle r=\frac{1}{2}d$

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

54π square inches

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

Calculator Click What You See Comment blinker clears screen
2 × × 3 × 6 +
2 × × 3 2*π*3*6+2*π*3² SA = 2πrh + 2πr² 54π Answer
###### Cylinder

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

169.6460033 square inches

See Toggle.
54π ⇔ 169.6460033

Calculator Click What You See Comment blinker clears screen
2 × × 3 × 6 +
2 × × 3 2*π*3*6+2*π*3² SA = 2πrh + 2πr² 54π 169.6460033 Answer
(Toggle)
###### Cylinder

Question

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

169.6 square inches

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?

1.2 square feet

See Measurement.
Square Feet = Square Inches ÷ 144
Square Feet = 169.6460033  ÷ 144 = 1.178097245 = 1.2 after rounding

Calculator Click What You See Comment blinker clears screen
2 × × 3 × 6 +
2 × × 3 2*π*3*6+2*π*3² SA = 2πrh + 2πr² 54π 169.6460033
169.6460033 ÷ 144 169.6460033÷144 Square Feet =
Square Inches ÷ 144 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?

402.12 cubic inches

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

Calculator Click What You See Comment blinker clears screen × 4 × 8 π*4²*8 V = πr²h 128π 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?

524.89 cubic inches $\bf\displaystyle r=\frac{1}{2}d$ $\bf\displaystyle r=\frac{1}{2}$* $\bf\displaystyle 8\frac{1}{2}$ $\bf\displaystyle\frac{17}{4}$

V = πr²h

V = π* $\bf\displaystyle{{\frac{17}{4}}^{2}}$* $\bf\displaystyle 9\frac{1}{4}$ $\bf\displaystyle\frac{10693\pi }{64}$ = 524.8914101 after toggle = 524.89 after rounding

Calculator Click What You See Comment blinker clears screen 1 2 ×  8 1 2  $\bf\displaystyle\frac{1}{2}$* $\bf\displaystyle 8\frac{1}{2}$ $\bf\displaystyle r=\frac{1}{2}d$  $\bf\displaystyle\frac{17}{4}$  r × 17 4  ×  9 1 4 π* $\bf\displaystyle{{\frac{17}{4}}^{2}}$* $\bf\displaystyle 9\frac{1}{4}$ V = πr²h  $\bf\displaystyle\frac{10693\pi }{64}$ 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?

113.1 square inches

LA = 2πrh
LA = 2 × π × 3 × 6 = 36π = 113.0973355 after toggle = 113.1 after rounding

Calculator Click What You See Comment blinker clears screen
2 × × 3 × 6 2*π*3*6 LA = 2πrh 36π 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?