# Surface Areas and Volumes Class 10 Maths Formulas

For those looking for help on Surface Areas and Volumes Class 10 Math Concepts can find all of them here provided in a comprehensive manner. To make it easy for you we have jotted the Class 10 Surface Areas and Volumes Maths Formulae List all at one place. You can find Formulas for all the topics lying within the Surface Areas and Volumes Class 10 Surface Areas and Volumes in detail and get a good grip on them. Revise the entire concepts in a smart way taking help of the Maths Formulas for Class 10 Surface Areas and Volumes.

## Maths Formulas for Class 10 Surface Areas and Volumes

The List of Important Formulas for Class 10 Surface Areas and Volumes is provided on this page. We have everything covered right from basic to advanced concepts in Surface Areas and Volumes. Make the most out of the Maths Formulas for Class 10 prepared by subject experts and take your preparation to the next level. Access the Formula Sheet of Surface Areas and Volumes Class 10 covering numerous concepts and use them to solve your Problems effortlessly.

**SURFACE AREA AND VOLUME OF COMBINATIONS**

**Cone on a Cylinder.**

r = radius of cone & cylinder;

h_{1} = height of cone

h_{2} = height of cylinder

Total Surface area = Curved surface area of cone + Curved surface area of cylinder + area of circular base

= πrl + 2πrh_{2} +πr^{2};

Slant height, l = \(\sqrt { { r }^{ 2 }+{ { { h }_{ 1 }^{ 2 } } } }\)

Total Volume = Volume of cone + Volume of cylinder

= \(\frac { 1 }{ 3 } { \pi r }^{ 2 }{ h }_{ 1 }+{ \pi r }^{ 2 }{ h }_{ 2 }\)

**Cone on a Hemisphere:**

h = height of cone;

l = slant height of cone = \(\sqrt { { r }^{ 2 }+{ h }^{ 2 } }\)

r = radius of cone and hemisphere

Total Surface area = Curved surface area of cone + Curved surface area of hemisphere = πrl + 2πr^{2}

Volume = Volume of cone + Volume of hemisphere = \(\frac { 1 }{ 3 } { \pi r }^{ 2 }h+\frac { 2 }{ 3 } { \pi r }^{ 3 }\)

**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 + πr^{2} + πrl

Volume = Volume of cylinder – Volume of cone = \({ \pi r }^{ 2 }h-\frac { 1 }{ 3 } { \pi r }^{ 2 }h=\frac { 2 }{ 3 } { \pi r }^{ 2 }h\)

**Cones on Either Side of Cylinder.**

r = radius of cylinder and cone;

h_{1} = height of cylinder

h_{2} = height of cones

Slant height of cone, l = \(\sqrt { { h }_{ 2 }^{ 2 }+{ r }^{ 2 } }\)

Surface area = Curved surface area of 2 cones + Curved surface area of cylinder = 2πrl + 2πrh_{1}

Volume = 2(Volume of cone) + Volume of cylinder = \(\frac { 2 }{ 3 } { \pi r }^{ 2 }{ h }_{ 2 }+{ \pi r }^{ 2 }{ h }_{ 1 }\)

**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 + 4πr^{2}

Volume = Volume of cylinder + Volume of 2 hemispheres = \({ \pi r }^{ 2 }h+\frac { 4 }{ 3 } { \pi r }^{ 3 }\)

**Hemisphere on Cube or Hemispherical Cavity on Cube**

a = side of cube;

r = radius of hemisphere.

Surface area = Surface area of cube – Area of hemisphere face + Curved surface area of hemisphere

= 6a^{2} – πr^{2} + 2πr^{2} = 6a^{2} + πr^{2}

Volume = Volume of cube + Volume of hemisphere = \({ a }^{ 3 }+\frac { 4 }{ 3 } { \pi r }^{ 3 }\)

**Hemispherical Cavity in a Cylinder**

r = radius of hemisphere;

h = height of cylinder

Total surface area = Curved surface area of cylinder + Surface area of base + Curved surface area of hemisphere

= 2πrh + πr^{2} + 2πr^{2} = 2πrh + 3πr^{2}

Volume = Volume of cylinder – Volume of hemisphere = \({ \pi r }^{ 2 }h-\frac { 2 }{ 3 } { \pi r }^{ 3 }\)