Question

Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting
cuboid.
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Answer 1

$\bf{\underline{Question:-}}$

Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting

cuboid.

$\bf{\underline{Solution:-}}$

We Know that ,

• Volume of Cube = a³

→ a³ = 512

→ a = $\sf \sqrt[3]{512}$

→ a = 8

→ Side (a) = 8

So ,

• Total Length = 8 + 8

→ Total length = 16cm

→ Total Breadth = 8

→ Total Height = 8

• Find Total Surface area of the Cuboid

• TSA of Cuboid = 2 ( lb + bh + hl)

→ 2 ( 16 * 8 + 8 * 8 + 8 * 16 )

→ 2 ( 128 +64 + 128 )

→ 2 (320)

→ 640 cm²

• Find Lateral Surface area

• Lateral Surface area = 2h ( L + b )

→ 2 * 8 ( 16 + 8)

→ 16 * 24

→ 384 cm²

$\bf{\underline{Hence:-}}$

• Surface area of resulting cuboid 384 cm²

_____________________

Answer 2

We Know that ,

Volume of Cube = a³

→ a³ = 512

→ a = \sf 3\sqrt{512}3

512

→ a = 8

→ Side (a) = 8

So ,

Total Length = 8 + 8

→ Total length = 16cm

→ Total Breadth = 8

→ Total Height = 8

Find Total Surface area of the Cuboid

TSA of Cuboid = 2 ( lb + bh + hl)

→ 2 ( 16 * 8 + 8 * 8 + 8 * 16 )

→ 2 ( 128 +64 + 128 )

→ 2 (320)

→ 640 cm²

Find Lateral Surface area

Lateral Surface area = 2h ( L + b )

→ 2 * 8 ( 16 + 8)

→ 16 * 24

→ 384 cm²