# Surface Areas and Volumes class 10 Notes Mathematics

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## 10 Mathematics notes Chapter 13 Surface Areas and Volumes

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CBSE Class 10 Mathematics
Revision Notes
CHAPTER 13
SURFACE AREAS AND VOLUMES

1. Surface Area of a Combination of Solids
2. Volume of a Combination of Solids
3. Conversion of Solid from One Shape to Another
4. Frustum of a Cone
5. Miscllaneous Questions

CUBOID

1. Surface area of cuboid  = $2\left( {lb + bh + hl} \right)$ sq. units
2. Volume of Cuboid = $lbh$ cubic units

CUBE

1. Surface area of cube = $6{s^2}$ sq. units
2. Volume of cube = ${s^3}$ cubic units

CYLINDER

1. Curved surface area of cylinder of radius r and height $h = 2\pi rh$ square units.
2. Total surface area of cylinder of radius r and height ${\text{h }} = {\text{ 2}}\pi {\text{r }}\left( {{\text{r }} + {\text{ h}}} \right)$square units.
3. Volume of cylinder of radius r and height $h = \pi {r^2}h$  cubic units.

CONE

1. Curved surface area of cone of radius r, height h and slant height $l = \pi rl$ square units where $l = \sqrt {{r^2} + {h^2}}$
2. Total surface area of cone of radius r, slant height $l$ = $\pi r\left( {l + r} \right)$  sq. units.
3. Volume of cone of radius r, height h $= \frac{1}{3}\pi {r^2}h$ cubic units.

SPHERE

1. Total surface area of sphere of radius ${\text{r units }} = {\text{ 4}}\pi {{\text{r}}^2}{\text{sq}}.$ units.
2. Volume of sphere of radius r units $= \frac{4}{3}\pi {r^3}$ cubic units.

HEMISPHERE

1. Curved surface area of hemisphere of radius ${\text{r units }} = {\text{ 2}}\pi {{\text{r}}^2}{\text{sq}}.$ units.
2. Total surface area of a solid hemisphere of radius ${\text{r units }} = {\text{ 3}}\pi {{\text{r}}^2}{\text{sq}}.$ units.
3. Volume of hemisphere of radius r units $= \frac{2}{3}\pi {r^3}$ cubic units.

FRUSTUM

1. Curved surface area of frustum = $\pi l(r + R)$ sq. units. Where $l$ slant height of frustum and radii of circular ends are r and R.
2. Total surface area of frustum $= \;\pi l(r + R) + \pi ({r^2} + {R^2})\;$sq. units.
3. Volume of Frustum =$= \frac{1}{3}\pi h({r^2} + {R^2} + rR)$ cubic units.
4. $l = \sqrt {{h^2} + {{(R - r)}^2}}$ units