Truncated Cone Calculator

Calculate volume and surface area of a frustum of right circular cone

and surface to volume ratio of a frustum of right circular cone

Definition of a frustum of a right circular cone: A frustum of a right circular cone (a truncated cone) is a geometrical figure that is created from a right circular cone by cutting off the tip of the cone perpendicular to its height H. The small h is the height of the truncated cone.

Radius base, R:Radius top, r:height, h:in:
precision: Surface to volume | Convert 564.44 inch³ to weight for: compounds | foods | gravels

show all units

The volume of the
truncated cone
= 564.44

centimeter³	9 249.51
foot³	0.33
inch³	564.44
meter³	0.01

The surface to volume ratio of this truncated cone
= 0.69

Surface area to volume ratio is also known as surface to volume ratio and denoted as sa÷vol, where sa is the surface area and vol is the volume.

show all units

α

degree

79.7

radian

1.39

Unit all	The area of the surface of the truncated cone
Unit all	A_base = 78.54	A_top = 28.27	A_lateral = 280.99	A_total = 387.81
centimeter²	506.71	182.41	1 812.85	2 501.97
foot²	0.55	0.2	1.95	2.69
inch²	78.54	28.27	280.99	387.81
meter²	0.05	0.02	0.18	0.25

Unit all	Height H = 27.5	Apothem l = 11.18
centimeter	69.85	28.4
foot	2.29	0.93
inch	27.5	11.18
meter	0.7	0.28

Unit all	The radii and height of the truncated cone
Unit all	R_base = 5	r_top = 3	height h = 11
centimeter	12.7	7.62	27.94
foot	0.42	0.25	0.92
inch	5	3	11
meter	0.13	0.08	0.28

Unit all	The diameters of the truncated cone
Unit all	D_base = 10	d_top = 6
centimeter	25.4	15.24
foot	0.83	0.5
inch	10	6
meter	0.25	0.15

About this page: Truncated Cone Calculator
- How to find the volume of a truncated cone?
  V = ⅓π×h×(R²+r²+R×r)
- How to find the area of the surface of a truncated cone?
  - How to find the area of the base surface of a truncated cone?
    A_base = π×R²
  - How to find the area of the top surface of a truncated cone?
    A_top = π×r²
  - How to find the area of the lateral surface of a truncated cone?
    A_lateral = π×l×(R+r) = π×(R+r)×√h²+(R−r)²
  - How to find the area of the total surface of a truncated cone?
    A_total = A_base+A_top+A_lateral
- How to find the surface to volume ratio of a truncated cone?
  SA÷V = A_total ⁄ V
- How to find the height of the original right cicular cone?
  H = h×(1+r ⁄ (R−r))
- How to find the apothem of a truncated cone?
  l = √h²+(R−r)²
- How to find the angle (α) between the radius of the base (R_base) and the apothem (l) of a truncated cone?
  α = arcsin(h ⁄ l)
- How to find the radii and diameters of a truncated cone?
  - How to find the radius of the base of a truncated cone?
    R_base = ½D_base
  - How to find the radius of the top of a truncated cone?
    r_top = ½d_top
  - How to find the diameter of the base of a truncated cone?
    D_base = 2×R_base
  - How to find the diameter of the top of a truncated cone?
    d_top = 2×r_top
- where:
  - R is the radius of the base circle;
  - r is the radius of the top circle;
  - h is the height or distance between the centers of the base and the top circles;
  - l is the apothem or distance between any two closest points on the base and the top circles;
  - H is the distance between the center of the base circle and the imaginary point that connects all apothems.
  Notes:
  - i. The big H is always greater than the small h.
  - ii. The top circle of the truncated cone is parallel to its base circle.
- The value of π.
  The pi (π) is approximately equal to 3.14159265359 and represents the ratio of any circle's circumference to its diameter, or the ratio of a circle's area to the square of its radius in Euclidean space.

Foods, Nutrients and Calories

SWEET GHERKINS, UPC: 009300005210 contain(s) 107 calories per 100 grams (≈3.53 ounces) [ price ]

768 foods that contain Vitamin B-12, added. List of these foods starting with the highest contents of Vitamin B-12, added and the lowest contents of Vitamin B-12, added, and Recommended Dietary Allowances (RDAs) for Vitamin B12

Gravels, Substances and Oils

CaribSea, Freshwater, Super Naturals, Blue Ridge weighs 1 826.1 kg/m³ (113.9997 lb/ft³) with specific gravity of 1.8261 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindrical, quarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]

Brain weighs 1 030 kg/m³ (64.3008 lb/ft³) [ weight to volume | volume to weight | price | density ]

Volume to weight, weight to volume and cost conversions for Sunflower oil with temperature in the range of 10°C (50°F) to 140°C (284°F)

Weights and Measurements

gram per square angstrom (g/Å²) is a metric measurement unit of surface or areal density

Dynamic viscosity is a measure of how resistive a fluid is to flow. Viscosity describes how thick a fluid is

YC to fC conversion table, YC to fC unit converter or convert between all units of electric charge measurement.

Calculators

Online Food Calories and Nutrients Calculator