Volume of a Cone calculator

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

l2=r2+h2 $l^2 = r^2 + h^2$

h2=l2-r2 $h^2 = l^2 - r^2$

h2=52-32 $h^2 = 5^2 - 3^2$

h2=16 $h^2 = 16$

h=4 $h = 4$

Volume=πr2h3 $"Volume" = (pi r^2 h)/3$

=π⋅32⋅43 $= (pi * 3^2 * 4)/3$

=37.6991 $= 37.6991$

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

=π⋅3(5+3) $= pi * 3 (5 + 3)$

=75.3982 $= 75.3982$

Curved Surface Area=πrl $"Curved Surface Area" = pi r l$

=π⋅3⋅5 $= pi * 3 * 5$

=47.1239 $= 47.1239$

Volume

1. Cuboid

Diagonal

(d)=√l2+b2+h2 $(d) = sqrt(l^2+ b^2+ h^2)$
Surface Area

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

(V)=lbh $(V) = lbh$

2. Cube

diameter

(d)=√2l $(d) = sqrt(2) l$
Diagonal

=√3l $= sqrt(3) l$
Surface Area

(SA)=6l2 $(SA) = 6 l^2$
Volume

(V)=l3 $(V) = l^3$

3. Cylinder

Curved Surface Area

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

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

(V)=πr2h $(V) = pi r^2 h$

4. Cone

Height

(h)=√l2-r2 $(h) = sqrt(l^2 - r^2)$
Curved Surface Area

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

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

(V)=πr2h3 $(V) = (pi r^2 h)/3$

5. Sphere

Surface Area

(SA)=4πr2 $(SA) = 4 pi r^2$
Volume

(V)=43πr3 $(V) = 4/3 pi r^3$
diameter

(d)=2r $(d) = 2r$

6. Hemisphere

Curved Surface Area

(CSA)=2πr2 $(CSA) = 2 pi r^2$
Total Surface Area

(TSA)=3πr2 $(TSA) = 3 pi r^2$
Volume

(V)=23πr3 $(V) = 2/3 pi r^3$
diameter

(d)=2r $(d) = 2r$

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) $"Here, we have " l = 3, b=4, h=5" (Given)"$ Diagonal2=l2+b2+h2 $"Diagonal"^2 = l^2 + b^2 + h^2$ Diagonal2=32+42+52 $"Diagonal"^2 = 3^2 + 4^2 + 5^2$ Diagonal2=50 $"Diagonal"^2 = 50$ Diagonal=7.0711 $Diagonal = 7.0711$ Here, we have l=3,b=4,h=5 (Given) $"Here, we have " l = 3, b=4, h=5" (Given)"$ Volume=l⋅b⋅h $"Volume" = l * b * h$ =3⋅4⋅5 $= 3 * 4 * 5$ =60 $= 60$ Here, we have l=3,b=4,h=5 (Given) $"Here, we have " l = 3, b=4, h=5" (Given)"$ Total Surface Area=2(lb+bh+lh) $"Total Surface Area" = 2 (lb + bh + lh)$ =2⋅(3⋅4+4⋅5+3⋅5) $= 2 * (3 * 4 + 4 * 5 + 3 * 5)$ =2⋅(47) $= 2 * (47)$ =94 $= 94$ Here, we have l=3,b=4,h=5 (Given) $"Here, we have " l = 3, b=4, h=5" (Given)"$ Curved Surface Area=2h(l+b) $"Curved Surface Area" = 2h (l + b)$ =2⋅5(3+4) $= 2 * 5 (3 + 4)$ =70 $= 70$

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 $"Here, we have " l = 3$ Diagonal=√3l $"Diagonal" = sqrt(3) l$ =√3⋅3 $= sqrt(3) * 3$ =5.1962 $= 5.1962$ Here, we have l=3 $"Here, we have " l = 3$ Volume=l3 $"Volume" = l^3$ =33 $= 3^3$ =27 $= 27$ Here, we have l=3 $"Here, we have " l = 3$ Total Surface Area=6l2 $"Total Surface Area" = 6 l^2$ =6⋅32 $= 6 * 3^2$ =6⋅9 $= 6 * 9$ =54 $= 54$ Here, we have l=3 $"Here, we have " l = 3$ Curved Surface Area=4l2 $"Curved Surface Area" = 4 l^2$ =4⋅32 $= 4 * 3^2$ =4⋅9 $= 4 * 9$ =36 $= 36$

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) $"Here, we have Radius "(r) = 3" and Height "(h) = 10" (Given)"$ Volume=πr2h $"Volume" = pi r^2 h$ =π⋅32⋅10 $= pi * 3^2 * 10$ =282.7433 $= 282.7433$ Total Surface Area=2πr(r+h) $"Total Surface Area" = 2 pi r (r+h)$ =2⋅π⋅3⋅(3+10) $= 2 * pi * 3 * (3 + 10)$ =245.0442 $= 245.0442$ Curved Surface Area=2πrh $"Curved Surface Area" = 2 pi r h$ =2⋅π⋅3⋅10 $= 2 * pi * 3 * 10$ =188.4956 $= 188.4956$

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) $"Here, we have Radius "(r) = 3" and Slant Height " (l) = 5" (Given)"$ l2=r2+h2 $l^2 = r^2 + h^2$ h2=l2-r2 $h^2 = l^2 - r^2$ h2=52-32 $h^2 = 5^2 - 3^2$ h2=16 $h^2 = 16$ h=4 $h = 4$ Volume=πr2h3 $"Volume" = (pi r^2 h)/3$ =π⋅32⋅43 $= (pi * 3^2 * 4)/3$ =37.6991 $= 37.6991$ Total Surface Area=πr(l+r) $"Total Surface Area" = pi r (l + r)$ =π⋅3(5+3) $= pi * 3 (5 + 3)$ =75.3982 $= 75.3982$ Curved Surface Area=πrl $"Curved Surface Area" = pi r l$ =π⋅3⋅5 $= pi * 3 * 5$ =47.1239 $= 47.1239$

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) $"Here, we have Radius"(r) = 3" (Given)"$ Volume=43πr3 $"Volume" = 4/3 pi r^3$ =43⋅π⋅33 $= 4/3 * pi * 3^3$ =84.823 $= 84.823$ Total Surface Area=4πr2 $"Total Surface Area" = 4 pi r^2$ =4⋅π⋅32 $= 4 * pi * 3^2$ =113.0973 $= 113.0973$ Curved Surface Area=4πr2 $"Curved Surface Area" = 4 pi r^2$ =4⋅π⋅32 $= 4 * pi * 3^2$ =113.0973 $= 113.0973$

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) $"Here, we have Radius " (r) = 3" (Given)"$ Volume=23πr3 $"Volume" = 2/3 pi r^3$ =23⋅π⋅33 $= 2/3 * pi * 3^3$ =56.5487 $= 56.5487$ Total Surface Area=3πr2 $"Total Surface Area" = 3 pi r^2$ =3⋅π⋅32 $= 3 * pi * 3^2$ =84.823 $= 84.823$ Curved Surface Area=2πr2 $"Curved Surface Area" = 2 pi r^2$ =2⋅π⋅32 $= 2 * pi * 3^2$ =56.5487 $= 56.5487$