Question

Four identical cubes, each of edge 4.5 cm, are joined end-to-end.
Write the name and dimensions of the resulting shape.
Also, find its surface

Answer 1

Given:

✰ Four identical cubes, each of edge 4.5 cm, are joined end-to-end.

To find:

✠ The name of the resulting shape.

✠ The dimensions of the resulting shape.

✠ Surface area of resulting figure.

Solution:

✧ The figure formed will be a cuboid.

A cuboid is a solid bounded by six rectangular faces.

⤳ Length of the resulting cuboid = 4 × 4.5

( As there are four identical cubes, which are joined end-to-end. )

⤳ Length of the resulting cuboid = 18 cm

⤳ Breadth of the resulting cuboid = 4.5 cm

⤳ Height of the resulting cuboid = 4.5 cm

Now we will use formula of total surface area of a cuboid to calculate the total surface area of the resulting figure which is a cuboid. Putting the values in the formula and then doing the required calculations.

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

Here,

• l is the length of the resulting cuboid.
• b is the breadth of the resulting cuboid.
• h is the height of the resulting cuboid.

Putting the values in the formula, we have:

➤ Surface area of a cuboid = 2( 18 × 4.5 + 4.5 × 4.5 + 4.5 × 18 )

➤ Surface area of a cuboid = 2( 81 + 20.25 + 81 )

➤ Surface area of a cuboid = 2 × 182.25

➤ Surface area of a cuboid = 364.5 cm²

∴ Surface area of resulting figure = 364.5 cm²

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