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Surface areas and volumes

Tutormate > CBSE Syllabus-Class 10th Maths > Surface areas and volumes

13 SURFACE AREAS AND VOLUMES

Shape	Figure	Curved surface area	Total surface area	Volume
Cube		$4 a^{2}$	$6 a^{2^{}}$	$a^{3}$
Cuboid		2h(1 + b)	(1b+bh+1h)	1bh
cylinder		$2 πrh$	$2 πr (r + h)$	${πr}^{2} h$
Right circular cone	l²=r²+h²	$πr 1$	$πr 1 + {πr}^{2} = πr (1 + r)$	$\frac{1}{3} {πr}^{2} h$
Sphere			$4 {πr}^{2}$	$\frac{4}{3} {πr}^{3}$
Hemispere		$2 {πr}^{2}$	$3 {πr}^{2}$	$\frac{2}{3} {πr}^{3}$
Frustrum		$π (r_{1} + r_{2}) 1$	$= π (r_{1} + r_{2}) 1 + {πr}_{1}^{2} + π$	$\frac{1}{3} πh (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2})$

Some more formula:

Cube:

D i a g o n a l o f t h e c u b e = \sqrt{3} a u n i t s

Cuboid:

D i a g o n a l o f t h e c u b o i d = \sqrt{1^{2} + b^{2} + h^{2}} u n i t s .

A r e a o f f o u r w a l l s o f a r o o m = 1 h + 1 h + b h + b h = 2 (1 + b) h

Right circular hollow cylinder:

Let R and r be the external and internal radii of a hollow cylinder of height h. Then,

(i) A r e a o f e a c h e n d = (R^{2} - r^{2})

(i i) C u r v e d s u r f a c e a r e a o f h o l l o w c y l i n d e r

= External surface area + Internal surface area

= 2 πRh + 2 πrh

= 2 πh (R + r)

(i i i) T o t a l s u r f a c e a r e a = 2 πRh + 2 πrh + 2 ({πR}^{2} - {πr}^{2})

= 2 πh (R + r) + 2 π (R + r) (R - r)

= 2 π (R + r) (R + h - r)

(i v) V o l u m e o f m a t e r i a l = E x t e r n a l v o l u m e - I n t e r n a l v o l u m e

= {πR}^{2} h - {πr}^{2} h

= πh (R^{2} - r^{2})

Spherical shell:

If R and r are respectively the outer and inner radii of a spherical shell, then

(i) O u t e r s u r f a c e a r e a = 4 {πR}^{2}

(i i) V o l u m e o f m a t e r i a l = 4 π (R^{3} - r^{3})

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