Choose language

Cone calculator - volume, surface area, generatrix, radius of base

The cone calculator will help you calculate the volume of the cone, the total area of the cone, the side area of the cone, the base area of the cone, the generatrix length and the radius of the cone base, and the volume of the sphere described on the cone.

Slant height (generatrix) of the cone - calculator

$$ l = \sqrt {h^2 + r^2} $$
What do you want to calculate ?

Lateral surface area of the cone - calculator

$$ P_{b} = \pi \cdot r \cdot l $$
What do you want to calculate ?

Base area of the cone - calculator

$$ P_{p} = \pi \cdot r^2 $$

radius (r)

Number of decimal places

Surface area of the cone - calculator

$$ P_{c} = P_{b} + P_{p}$$ $$ P_{c} = \pi r l + \pi r^2 = \pi r(r + l) $$

generatrix (slant height) (l)

radius (r)

Number of decimal places

Volume of the cone - calculator

$$ V = \frac{1}{3}P_{p} \cdot h = \frac{\pi r h}{3} $$
What do you want to calculate ?

Volume of the sphere described on the cone - calculator

$$ V_{k} = \frac{1}{6} \pi \frac{l^6}{(l^2 - r^2) \sqrt{l^2 - r^2}} $$

generatrix (slant height) (l)

radius (r)

Number of decimal places

Cone - information

Right circular cone is a convex solid formed by the rotation of a right triangle around one of the legs (cathetuses). This cathetus creates the height (h) of the cone, the other leg (cathetus) becomes the radius of the base (r), and the hypotenuse - slant height of the cone (l).

Slant height of the cone

Slant height follows from the Pythagorean theorem:
$$ l=\sqrt {h^{2}+r^{2}} $$

Lateral surface area of the cone

Lateral surface of the cone, after it is stretched on the plane, forms a circular segment with a radius R = l as the slant height of the cone and the arc length equal to the circumference of the cone base L=2πr
A circular segment with radius R and arc length L has an area: $$ P=\frac {1}{2}LR $$ hence $$ P_{b}=\frac {1}{2}LR=\frac {1}{2}2\pi rl=\pi rl $$

Base area of the cone

The base of the cone is formed by a circle with a radius r. $$ P_{p} = \pi r^2 $$

Surface area of the cone

$$ P_{c} = P_{b} + P_{p} $$ hence $$ P_{c} = \pi r l + \pi r^2 = \pi r(r + l) $$

Volume of the cone

$$ V = \frac{1}{3}P_{p}h = \frac{\pi r^2 h}{3} $$

Volume of the sphere described on the cone

$$ V_{k} = \frac{1}{6} \pi \frac{l^6}{(l^2 - r^2) \sqrt{l^2 - r^2}} $$

Users of this calculator also used

Rail Fence, Zig-Zag - encoder / decoder

Rail Fence, Zig-Zag cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Rail Fence, Zig-Zag cipher.

Quartiles Q1, Q2, Q3 of the interval series

With this statistical calculator, you will learn how to calculate the lower quartile, middle quartile, and upper quartile of an interval resolution series.

Mean square, arithmetic mean of the squares, power mean of second order

With this calculator you will calculate the mean square or arithmetic mean of the squares also known as the power mean of the second order.

Assessment of the fit of the diet and exercise plan - test

Is the chosen weight loss plan adjusted to your needs and possibilities and will it bring the expected results?

The key to success in dietary plans is its proper selection. However, too often we choose plans that are not tailored to us, resulting in ineffectiveness and discouragement, and consequently the quick abandonment of the plan.

Use this test to find out also what factors a tailored diet plan should contain and training sessions. And it's best to apply this test to the already selected plan so as not to waste time on a wrong diet and training.

Calculator for maximum heart rate and heart rate zones for training

How to calculate your Maximum Heart Rate (HRMAX)? Which heart rate zones to choose for training and how to calculate the heart rate zones? At what heart rate is the best fat burning, and at what will we increase our efficiency and improve the condition? The calculator for maximum heart rate and heart rate zones can help answer these questions. You will calculate both your maximum and optimal heart rate and select the heart rate ranges for the appropriate training.

Force, mass and acceleration calculator

With this calculator you can calculate the force, mass and acceleration from Newton's Second Law of Motion.

ROT47 cipher - encoder / decoder

ROT47 cipher online encoder and decoder. Encrypt and decrypt any cipher created in a ROT47 cipher. You can use any shift and additionally a key for more precise text encoding.

Online calculator

M+

M-

log

10^x

asin

acos

atan

e^x

sin^-1

cos^-1

tan^-1

sin

cos

tan

√

x²

1/x

x^M

(

)

exp

M+

M-

sin

sin^-1

asin

cos

cos^-1

acos

log

10^x

tan

tan^-1

atan

e^x

exp

1/x

(

)

x^M

x²

√