Cone = ThreeDimensional 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 
blinker  clears screen  
π × 6 × 10 + π × 6  π*6*10+π*6²  SA = πrs + πr² 
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 
blinker  clears screen  
π × 6 × 10 + π × 6  π*6*10+π*6²  SA = πrs + πr² 
96π  
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 
blinker  clears screen  
π × 6 × 10 + π × 6  π*6*10+π*6²  SA = πrs + πr² 
96π  
301.5928947  
301.5928947 ÷ 144  301.5928947÷144  Square Feet = Square Inches ÷ 144 square inches per square foot 
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 
blinker  clears screen  
1 3 × π × 3 × 4 
*π*3² *4  V = πr²h 
12π  
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 
blinker  clears screen  
1 2 × 6 1 2 
r =  
r  
1 3 × π × 13 4 × 4 1 4 
V = πr²h  
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 
blinker  clears screen  
π × 3 × 5  π*3*5  LA = πrs 
15π  
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