Height(h) of a Cone calculator

SolutionExampleVolume FormulaAll Problems

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. Hemi-Sphere

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 [ Hemi-Sphere ] Enter your problem 6. I know that for a Hemi-Sphere Radius = 3 . From this find out Volume of the Hemi-Sphere.


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`