CBSE Class 10th Maths

Surface Areas and Volumes

SURFACE AREA AND VOLUME OF COMBINATIONS

Cone on a Cylinder.

r = radius of cone & cylinder;
h1 = height of cone
h2 = height of cylinder
Total Surface area = Curved surface area of cone + Curved surface area of cylinder + area of circular base
= πrl + 2πrh2 +πr2;
Slant height, l =
Total Volume = Volume of cone + Volume of cylinder
1/3πr2h1+πr2h2

Cone on a Hemisphere:

h = height of cone;
l = slant height of cone =
r = radius of cone and hemisphere
Total Surface area = Curved surface area of cone + Curved surface area of hemisphere = πrl + 2πr2
Volume = Volume of cone + Volume of hemisphere = 1/3πr2h+2/3πr3

Conical Cavity in a Cylinder

r = radius of cone and cylinder;
h = height of cylinder and conical cavity;
l = Slant height
Total Surface area = Curved surface area of cylinder + Area of bottom face of cylinder + Curved surface area of cone = 2πrh + πr2 + πrl
Volume = Volume of cylinder – Volume of cone =

Cones on Either Side of Cylinder.

r = radius of cylinder and cone;
h1 = height of cylinder
h2 = height of cones
Slant height of cone, l =
Surface area = Curved surface area of 2 cones + Curved surface area of cylinder = 2πrl + 2πrh1
Volume = 2(Volume of cone) + Volume of cylinder = 2/3πr2h2+πr2h1

Cylinder with Hemispherical Ends.

r = radius of cylinder and hemispherical ends;
h = height of cylinder
Total surface area= Curved surface area of cylinder + Curved surface area of 2 hemispheres = 2πrh + 4πr2
Volume = Volume of cylinder + Volume of 2 hemispheres = πr2h+4/3πr3

Hemisphere on Cube or Hemispherical Cavity on Cube

a = side of cube;