The volume of a cube is 512 cm3.Find its lateral surface area.

1.	The volume of a cube is 512 cm3.Find its lateral surface area.
Answer» ANSWER: $\red\star$ Lateral Surface AREA of the Cube = 384cm². SOLUTION Given:- Volume of a Cube = 512cm³. To FIND :- Its lateral surface area. ANSWER Equation for Volume of Cube = a³(Where 'a' is the side of the cube) $\implies$ a³ = 512 $\implies$ $\sf a = \sqrt[3]{512}$ $\implies$ a = 8 cm. Side of the Cube (a) = 8cm. Diagram $\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 8cm}\put(13.5,3){\bf\large 8cm}\put(-4,5.8){\bf\large 8cm}\end{picture}$ LATERAL SURFACE AREA Lateral Surface Area (LSA) of a cube = 4a²(Where 'a' is the side of the cube) Here , a = 8cm. $\implies$ LSA of the Cube = 4 × 8² $\implies$ LSA of the Cube = 4 × 64 $\implies$ LSA of the Cube = 256cm². LATERAL SURFACE AREA OF SOME OTHER SHAPES CUBOID LSA = 2(l+b)×h CYLINDER LSA = 2πrh CONE LSA = πrl SPHERE LSA = 4πr²

Answer»

ANSWER:

$\red\star$ Lateral Surface AREA of the Cube = 384cm².

SOLUTION

Given:-

Volume of a Cube = 512cm³.

To FIND :-

Its lateral surface area.

ANSWER

Equation for Volume of Cube = a³(Where 'a' is the side of the cube)

$\implies$ a³ = 512

$\implies$

$\sf a = \sqrt[3]{512}$

$\implies$ a = 8 cm.

Side of the Cube (a) = 8cm.

Diagram

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 8cm}\put(13.5,3){\bf\large 8cm}\put(-4,5.8){\bf\large 8cm}\end{picture}$

LATERAL SURFACE AREA

Lateral Surface Area (LSA) of a cube = 4a²(Where 'a' is the side of the cube)

Here ,

a = 8cm.

$\implies$ LSA of the Cube = 4 × 8²

$\implies$ LSA of the Cube = 4 × 64

$\implies$ LSA of the Cube = 256cm².

LATERAL SURFACE AREA OF SOME OTHER SHAPES

CUBOID

LSA = 2(l+b)×h

CYLINDER

LSA = 2πrh

CONE

LSA = πrl

SPHERE

LSA = 4πr²