If two identical cubes are joined end to end together, then what is the length of resulting cuboid?

Question 12 Volume Surface Area Cuboid Cube Exercise 21.4

Answer:

Given details are,

Volume of each cube = 512 cm3

Let length of edge of each cube be ‘a’ cm

So,

Edge, a3 = 512 a = 3√512

= 8cm

When these two cubes are joined end to end, a cuboid is formed.

Length of cuboid = 8+8 = 16 cm

Breadth = 8 cm Height = 8 cm

Surface area of resulting cuboid = 2 (lb + bh + hl)

= 2 (16×8 + 8×8 + 8×16)

= 2 (128 + 64 + 128)

= 2 (320)

= 640 cm2

∴ Surface area of resulting cuboid is 640cm2.

Video transcript

hello welcome to leader learning today we are going to see a question that is z upon 3 minus 1 equals to 5 minus 5 so we need to find the z value 0 upon 3 equals to minus 5 plus 1 0.3 equals to minus 4 z equals to 3 into minus 4 is that equals to minus 12 the final value of that is minus 12 i hope you understand this video thank you for watching this video

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150 Questions 100 Marks 180 Mins

Given:

Volume of each identical cube = 64 cm3

And the number of cube = 2

Formula used:

If the cube of a side length x, then the volume of cube = x3

If the cuboid have length(l), breadth(b) and height(h), then total surface area of cuboid = 2 × [(l × b) + (b × h) + (h × l)]

Calculation:

The volume of cube = 64 cm3

⇒ x3 = 64

⇒ x = 4 cm

But the cuboid is made by joining end to end of the cube then the length of the cuboid will be twice the side length of each cube and the rest breadth and height will remain the same.

Thus, l = 2 × 4

⇒ l = 8 cm

Breadth(b) = 4 cm

And height = 4 cm

The total surface area of cuboid = 2 × [(8 × 4) + (4 × 4) + (4 × 8)]

⇒ 2 × [32 + 16 + 32]

⇒ 2 × [80]

⇒ 160 cm2

∴ The total surface area of cuboid is 160 cm2

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