Cone = Three-Dimensional Shape with Circular Base Connecting to a Point
Basics
r = radius = distance halfway across circular base of cone
d = diameter = distance all the way across circular base of cone
h = height
s = slant height = distance along cone’s side
Apex = point of cone
Base = circular portion of cone
SA = Surface Area = area covering surface, including base, of cone (measured in square units)
LA = Lateral Area = area covering surface, excluding base, of cone (measured in square units)
V = Volume = space occupied by cone (measured in cubic units)
Formulas (Mathematics Formula Sheet)
SA = πrs + πr²
V = πr²h
Formulas (NOT on Mathematics Formula Sheet)
LA = πrs
r =
Question
A solid highway cone has a radius of 6 inches, height 8 inches, and slant height 10 inches. What is its surface area?
Answer
96π square inches
Answer Process
SA = πrs + πr²
SA = π × 6 × 10 + π × 6² = 96π
Input | Display | Comment |
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blinker | clears screen |
π × 6 × 10 + π × 6 ![]() |
π*6*10+π*6² | SA = πrs + πr² |
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96π | Answer |
Cone |
Question
With reference to the question above, what is the area of the cone in decimal form?
Answer
301.5928947 square inches
Answer Process
See Toggle.
96π ⇔ 301.5928947
Input | Display | Comment |
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blinker | clears screen |
π × 6 × 10 + π × 6 ![]() |
π*6*10+π*6² | SA = πrs + πr² |
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96π | |
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301.5928947 | Answer |
Cone |
Question
With reference to the question above, what is the area of the cone to the nearest tenth?
Answer
301.6 square inches
Answer Process
See Rounding.
301.5928947 → 301.6
Question
A solid highway cone has a radius of 6 inches, height 8 inches, and slant height 10 inches. To the nearest tenth of a square foot, what is its surface area?
Answer
2.1 square feet
Answer Process
See Measurement.
Square Feet = Square Inches ÷ 144 square inches per square foot
Square Feet = 301.5928947 ÷ 144 = 2.094395102 = 2.1 after rounding
Input | Display | Comment |
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blinker | clears screen |
π × 6 × 10 + π × 6 ![]() |
π*6*10+π*6² | SA = πrs + πr² |
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96π | |
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301.5928947 | |
301.5928947 ÷ 144 | 301.5928947÷144 | Square Feet = Square Inches ÷ 144 square inches per square foot |
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2.094395102 | Answer (before rounding) |
Cone |
Question
A solid toy cone has a radius of 3 inches, height 4 inches, and slant height 4 inches. To the nearest hundredth of a cubic inch, what is its volume?
Answer
37.70 cubic inches
Answer Process
V = πr²h
V = x π x 3² x 4 = 37.69911184 after toggle = 37.70 after rounding
Input | Display | Comment |
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blinker | clears screen |
![]() ![]() × π × 3 ![]() |
V = |
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12π | |
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37.69911184 | Answer (before rounding) |
Cone |
Question
A solid highway cone has a diameter of inches, height
inches, and slant height
inches. To the nearest hundredth of a cubic inch, what is its volume?
Answer
47.01 cubic inches
Answer Process
r =
r = =
V = πr²h
V = =
= 47.00935257 after toggle = 47.01 after rounding
Input | Display | Comment |
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blinker | clears screen |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
r = |
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r | |
![]() ![]() ![]() ![]() ![]() ![]() × ![]() ![]() ![]() ![]() ![]() |
V = |
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||
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47.00935257 | Answer (before rounding) |
Cone |
Question
A solid highway cone has a radius of 3 inches, height 4 inches, and slant height 5 inches. To the nearest tenth of a square inch, what is its lateral area?
Answer
47.1 square inches
Answer Process
LA = πrs
LA = π × 3 × 5 = 47.1238898 after toggle = 47.1 after rounding
Input | Display | Comment |
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blinker | clears screen |
π × 3 × 5 | π*3*5 | LA = πrs |
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15π | |
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47.1238898 | Answer (before rounding) |
Cone |
Practice – Questions
1. A solid highway cone has a radius of 5 inches, height 12 inches, and slant height 13 inches. To the nearest tenth of a square inch, what is its surface area?
2. With reference to Question 2, what is the cone’s surface area to the nearest tenth of a square foot?
3. A cotton candy cone has a radius of 5 inches, height 12 inches, and slant height 13 inches. To the nearest hundredth of a cubic inch, what is its volume?
4. A cotton candy cone has a diameter of inches, height
inches, and slant height
inches. To the nearest hundredth of a cubic inch, what is its volume?
5. A cotton candy cone has a radius of 5 inches, height 12 inches, and slant height 13 inches. To the nearest tenth of a square inch, what is its lateral area?
Practice – Answers
1. 282.7 square inches
2. 2.0 square feet
3. 314.16 cubic inches
4. 353.58 cubic inches
5. 204.2 square inches