Question

The volume of a rectangular parallelopiped is twice the volume of a cube. If the length, breadth and height of the parallelopiped are 9cm, 8cm and 6cm respectively, then find the length of each side of the cube and also its surface area.​

Answer 1

Answer:

Step-by-step explanation:

To find the length of each side of the cube and its surface area

The volume of a rectangular parallel piped is twice the volume of a cube.

The dimensions of rectangular parallel piped are 9 cm[Length], 8 cm[Breadth] and 6 cm[Height]

Step = We know that rectangular parallel shape - is known as cuboid

Let the volume of cuboid(or rectangular parallel) be 'y'

And,

Let the volume of cube be '2x'[As per the condition of the question]

We know that volume of cuboid = Length(l) X Breadth(b) X Height(h)

And,

Volume of cube = Side X Side X Side(or $side^{3}$)

Length(l) = 9 cm(Given)

Breadth(b) = 8 cm(Given)

Height = 6 cm(Given)

Now equate the volume of cuboid[or rectangular parallel] with volume of cube as per the condition of the question

That is,

y = 2x

y = volume of cuboid = l X b X h

x = volume of cube = Side X Side X Side(or $side^{3}$)

l X b X h = 2x

9 X 8 X 6 = 2x

72 X 6 = 2x

432 = 2x

432/2 = x(using linear equation rules)

x = 216 $cm^{3}$(volume of cube = $side^{3}$)

So

Each side = $216^{1/3}$ or $\sqrt[3]{216}$

Each side = 6 cm(Length of each side of the cube)

We know that whenever it is asked to find surface area without specifying particularly we always take as total surface area(T.S.A)

Total surface area(T.S.A) o a cube = 6$l^{2}$

l = Length

In case of Cube

Length = Breadth = Height

= 6 cm(side or length or breadth or height)

Continue

T.S.A = 6$l^{2}$

         = 6$(6)^{2}$

         = 6(36)

T.S.A  = 216 $cm^{2}$[Total surface area of the cube]

Answer 2

Given : The volume of a rectangular parallelopiped is twice the volume of a cube. If the length, breadth and height of the parallelopiped are 9cm, 8cm and 6cm respectively,

To find : the length of each side of the cube and also its surface area.​

Solution:

Volume of a rectangular parallelopiped  = length * breadt * height

= 9 * 8 * 6

= 432

Volume of a rectangular parallelopiped = 2 * volume of a cube

=> volume of a cube = 432/2

=>  volume of a cube = 216  cm³

volume of a cube = Side³

=> Side³ = 216

=> Side = 6³

=> Side = 6  cm

length of each side of the cube   = 6 cm

surface area of cube = 6 (side)² = 6(6)² = 216  cm²

length of each side of the cube  = 6 cm

surface area of cube = 216  cm²

Learn more:

A man has solids of shapes (sphere, cube, cylinder, cuboid &amp ...

https://brainly.in/question/13532326

Anup arranged 72, 1 cm cubes in 4 layers with 9 of them lengthwise ...

https://brainly.in/question/8166442

a cube of side 24cm contains the same quantity of sugar as a ...

https://brainly.in/question/7342836