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Surface area of cube with rectangular prism dimensions - Rectangular Prism - Mensuration problem solver

A cube has the same volume as a rectangular prism whose dimensions are 6 units (length) by 12 units (width) by 24 units (height). What is the surface area of the cube?

Surface area of cube with rectangular prism dimensions

length = 6
width = 12
height = 24
V =  l * w * h
volume = 6 * 12 * 24
volume = 1728
So the volume is 1728
cube

Since the cube and the rectangular prism has same volume, finding the volume of one object is enough. From this we can find the side of the cube and then the volume.


volume = 1728
a =  pow( V ,(1/3))
side = pow( 1728 ,(1/3))
side = 12
So the side is 12
SA =  6 * a * a
surface area = 6 * 12 * 12
surface area = 864
So the surface area is 864

Rectangular prism Formulas :

LSA =  p * h

p =  2 * ( l + w )

V =  l * w * h

d =  sqrt( l * l + w * w + h * h )

h =  V / ( l * w )

l =  V / ( w * h )

w =  V / ( l * h )


where,

LSA = lateral surface area
TSA = total surface area
p = perimeter
h = height
V = volume
l = length
w = width
d = diagonal

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