Question

Two cubes each of 8 cm edge are joined end to end. Find the surface area of the resulting cuboid.​

Answer 1

Given -

• Edge of two cubes is 8cm

To find -

• Total surface area of resulting cuboid.

Formula used -

• Total surface area of cuboid.

Solution -

In the question, we are provided with the edge of two cubes i.e 8cm, and they are joined together from end to end. So, the length, Breadth and height of the resulting cuboid will be 8cm only, just the length will be different, as the cubes are joined from end to end, we will add 8cm to 8cm, after that we will further do this question.

According to question -

$\longrightarrow$ Length of cuboid = 8cm + 8cm = 16cm

$\longrightarrow$ Breadth of cuboid = 8cm

$\longrightarrow$ Height of cuboid = 8cm

Total surface area of cuboid -

$\sf \longrightarrow \: 2(lb \: + \: bh \: + hl)$

On substituting the values -

$\sf \longrightarrow \: TSA \: = 2(16cm)(8cm) \: + (8cm)(8cm) \: + (8cm)(16cm) \\ \\ \sf \longrightarrow \: TSA \: = 2(128cm\: + 64cm \: + 128cm) \\ \\ \sf \longrightarrow \: TSA \: = 2(320cm) \\ \\ \sf \: TSA \: = 640 {cm}^{2}$

$\therefore$ The total surface area of the resulting cuboid is 640cm²

2 more formulae (of cuboid)

1. Lateral surface area = 2h(l + b)

2. Volume = L × B × H

___________________________________________

Answer 2

Answer:

Given :-

• Two cubes each of 8 cm edge are joined end to end.

To Find :-

• What is the total surface area of the resulting cuboid.

Formula Used :-

${\red{\boxed{\small{\bold{T.S.A\: of\: cuboid =\: 2(LB + BH + HL)}}}}}$

where,

• T.S.A = Total Surface Area
• L = Length
• B = Breadth
• H = Height

Solution :-

Two cubes each of 8 cm edge are joined,

Then,

↛ 2(8 cm)

↛ 2 × 8 cm

➦ 16 cm

Hence, new length is 16 cm.

Given :

• Length = 16 cm
• Breadth = 8 cm
• Height = 8 cm

According to the question by using the formula we get,

⇒ $\sf T.S.A =\: 2(16 × 8 + 8 × 8 + 8 × 16)$

⇒ $\sf T.S.A =\: 2(128 + 64 + 128)$

⇒ $\sf T.S.A =\: 2(192 + 128)$

⇒ $\sf T.S.A =\: 2(320)$

⇒ $\sf T.S.A =\: 2 \times 320$

➠ $\sf\bold{\purple{T.S.A =\: 640\: {cm}^{2}}}$

${\underline{\boxed{\small{\bf{\therefore The\: total\: surface\: area\: of\: the\: resulting\: cuboid\: is\: 640\: {cm}^{2}.}}}}}$