Cylinder = ThreeDimensional 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 (Mathematics Formula Sheet)
SA = 2πrh+ 2πr²
V = πr²h
Formulas (NOT on Mathematics Formula Sheet)
LA = 2πrh
r =
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 
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?
Answer
169.6460033 square inches
Answer Process
See Toggle.
54π ⇔ 169.6460033
Input  Display  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?
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 
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 square inches per square foot 
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 
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 inches and height inches. To the nearest hundredth of a cubic inch, what is its volume?
Answer
524.89 cubic inches
Answer Process
r =
r = =
V = πr²h
V = π x = = 524.8914101 after toggle = 524.89 after rounding
Input  Display  Comment 
blinker  clears screen  
1 2 × 8 1 2 
r =  
r  
× 17 4 × 9 1 4 
π*  V = πr²h 
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 
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 inches and height 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