Question

if the volume of a cube is 4,096 what is the surface area

Answer 1

✺ AnsweR:-

Figure is given below ,

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(5.6,5.6){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.46,8.7){ D }\put(3.55,10.15){ E }\put(3.55,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){ a }\put(7.75,6.2){ a }\put(11.1,7.5){ a }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

$\blacksquare \:\:\:\red{\ \ {Volume= 4,096\:unit^3}}$

Now we know that , for a cube of side a unit ,

$\implies\ \ {Volume=side^3}$

$\implies\ \ {4096=a^3}$

$\implies\ \ {a=\sqrt[3]{4096} }$

$\implies\ \ {a=16\:unit }$

∴ Surface Area = 6×a² = ( 6×16²) = 1536 unit²

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

Answer 2

Answer:

16 m

Step by step explanation:

volume of cube =a ³ = 4096 m  ³

 so a=  ∛ 4096

​  =16 m.