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 (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 |
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2 × ![]() + 2 × ![]() ![]() |
2*π*3*6+2*π*3² | SA = 2πrh + 2πr² |
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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 |
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2 × ![]() + 2 × ![]() ![]() |
2*π*3*6+2*π*3² | SA = 2πrh + 2πr² |
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54π | |
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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 |
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blinker | clears screen |
2 × ![]() + 2 × ![]() ![]() |
2*π*3*6+2*π*3² | SA = 2πrh + 2πr² |
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54π | |
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169.6460033 | |
169.6460033 ÷ 144 | 169.6460033÷144 | Square Feet = Square Inches ÷ 144 square inches per square foot |
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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 |
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π*4²*8 | V = πr²h |
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128π | |
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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 |
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r = |
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r | |
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π* |
V = πr²h |
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||
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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 |
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blinker | clears screen |
2 × ![]() |
2*π*3*6 | LA = 2πrh |
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36π | |
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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