Volume of a Cone calculator

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Volume of a Cone

Height $(h) = sqrt(l^2 - r^2)$
Curved Surface Area $(CSA) = pi r l$
Total Surface Area $(TSA) = pi r (l + r)$
Volume $(V) = (pi r^2 h)/3$

Example :
I know that for a cone Radius = 3 and Slant Height = 5 . From this find out Volume of the cone.

$"Here, we have Radius "(r) = 3" and Slant Height " (l) = 5" (Given)"$

$l^2 = r^2 + h^2$

$h^2 = l^2 - r^2$

$h^2 = 5^2 - 3^2$

$h^2 = 16$

$h = 4$

$"Volume" = (pi r^2 h)/3$

$= (pi * 3^2 * 4)/3$

$= 37.6991$

$"Total Surface Area" = pi r (l + r)$

$= pi * 3 (5 + 3)$

$= 75.3982$

$"Curved Surface Area" = pi r l$

$= pi * 3 * 5$

$= 47.1239$

Volume

1. Cuboid

Diagonal

$(d) = sqrt(l^2+ b^2+ h^2)$
Surface Area

$(SA) = 2 (lb + bh + hl)$
Volume

$(V) = lbh$

2. Cube

diameter

$(d) = sqrt(2) l$
Diagonal

$= sqrt(3) l$
Surface Area

$(SA) = 6 l^2$
Volume

$(V) = l^3$

3. Cylinder

Curved Surface Area

$(CSA) = 2 pi r h$
Total Surface Area

$(TSA) = 2 pi r (r + h)$
Volume

$(V) = pi r^2 h$

4. Cone

Height

$(h) = sqrt(l^2 - r^2)$
Curved Surface Area

$(CSA) = pi r l$
Total Surface Area

$(TSA) = pi r (l + r)$
Volume

$(V) = (pi r^2 h)/3$

5. Sphere

Surface Area

$(SA) = 4 pi r^2$
Volume

$(V) = 4/3 pi r^3$
diameter

$(d) = 2r$

6. Hemisphere

Curved Surface Area

$(CSA) = 2 pi r^2$
Total Surface Area

$(TSA) = 3 pi r^2$
Volume

$(V) = 2/3 pi r^3$
diameter

$(d) = 2r$

Problem : 1 / 6 [ Cuboid ] Enter your problem 1. I know that for a cuboid Length = 3 , Breadth = 4 , and Height = 5 . From this find out Volume of the cuboid.


Solution:	$"Here, we have " l = 3, b=4, h=5" (Given)"$ $"Diagonal"^2 = l^2 + b^2 + h^2$ $"Diagonal"^2 = 3^2 + 4^2 + 5^2$ $"Diagonal"^2 = 50$ $Diagonal = 7.0711$ $"Here, we have " l = 3, b=4, h=5" (Given)"$ $"Volume" = l * b * h$ $= 3 * 4 * 5$ $= 60$ $"Here, we have " l = 3, b=4, h=5" (Given)"$ $"Total Surface Area" = 2 (lb + bh + lh)$ $= 2 * (3 * 4 + 4 * 5 + 3 * 5)$ $= 2 * (47)$ $= 94$ $"Here, we have " l = 3, b=4, h=5" (Given)"$ $"Curved Surface Area" = 2h (l + b)$ $= 2 * 5 (3 + 4)$ $= 70$

Problem : 2 / 6 [ Cube ] Enter your problem 2. I know that for a cube Length = 3 . From this find out Volume of the cube.


Solution:	$"Here, we have " l = 3$ $"Diagonal" = sqrt(3) l$ $= sqrt(3) * 3$ $= 5.1962$ $"Here, we have " l = 3$ $"Volume" = l^3$ $= 3^3$ $= 27$ $"Here, we have " l = 3$ $"Total Surface Area" = 6 l^2$ $= 6 * 3^2$ $= 6 * 9$ $= 54$ $"Here, we have " l = 3$ $"Curved Surface Area" = 4 l^2$ $= 4 * 3^2$ $= 4 * 9$ $= 36$

Problem : 3 / 6 [ Cylinder ] Enter your problem 3. I know that for a cylinder Radius = 3 and Height = 10 . From this find out Curved Surface Area of the cylinder.


Solution:	$"Here, we have Radius "(r) = 3" and Height "(h) = 10" (Given)"$ $"Volume" = pi r^2 h$ $= pi * 3^2 * 10$ $= 282.7433$ $"Total Surface Area" = 2 pi r (r+h)$ $= 2 * pi * 3 * (3 + 10)$ $= 245.0442$ $"Curved Surface Area" = 2 pi r h$ $= 2 * pi * 3 * 10$ $= 188.4956$

Problem : 4 / 6 [ Cone ] Enter your problem 4. I know that for a cone Radius = 3 and Slant Height = 5 . From this find out Volume of the cone.


Solution:	$"Here, we have Radius "(r) = 3" and Slant Height " (l) = 5" (Given)"$ $l^2 = r^2 + h^2$ $h^2 = l^2 - r^2$ $h^2 = 5^2 - 3^2$ $h^2 = 16$ $h = 4$ $"Volume" = (pi r^2 h)/3$ $= (pi * 3^2 * 4)/3$ $= 37.6991$ $"Total Surface Area" = pi r (l + r)$ $= pi * 3 (5 + 3)$ $= 75.3982$ $"Curved Surface Area" = pi r l$ $= pi * 3 * 5$ $= 47.1239$

Problem : 5 / 6 [ Sphere ] Enter your problem 5. I know that for a sphere Radius = 3 . From this find out Volume of the sphere.


Solution:	$"Here, we have Radius"(r) = 3" (Given)"$ $"Volume" = 4/3 pi r^3$ $= 4/3 * pi * 3^3$ $= 84.823$ $"Total Surface Area" = 4 pi r^2$ $= 4 * pi * 3^2$ $= 113.0973$ $"Curved Surface Area" = 4 pi r^2$ $= 4 * pi * 3^2$ $= 113.0973$

Problem : 6 / 6 [ Hemisphere ] Enter your problem 6. I know that for a Hemisphere Radius = 3 . From this find out Volume of the Hemisphere.


Solution:	$"Here, we have Radius " (r) = 3" (Given)"$ $"Volume" = 2/3 pi r^3$ $= 2/3 * pi * 3^3$ $= 56.5487$ $"Total Surface Area" = 3 pi r^2$ $= 3 * pi * 3^2$ $= 84.823$ $"Curved Surface Area" = 2 pi r^2$ $= 2 * pi * 3^2$ $= 56.5487$