Question

2 cubes each of volume 64cm3 are joined end to end find the surface area of resulting cubiode

Answer 1

$\huge\underline{\bf{Given}}$

Two volumes each of 64 cm³ are joined end to end formed a Cuboid.

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$\huge\underline{\bf{To\: Find}}$

Surface area of resulting cuboid.

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$\huge\underline{\bf{Solution}}$

It is given that

★ Volume of 1 cube = 64 cm³

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Volume\: of\: cube = (side)^3{\bigstar}}}}$

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Let the side of cube be a.

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$\tt\longmapsto{a^3 = 64}$

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$\tt\longmapsto{a = \sqrt[3]{64}}$

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$\tt\longmapsto{a = 4 cm}$

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★ Now

• Length of Cuboid = 4 + 4 = 8cm
• Breadth of Cuboid = 4cm
• Height of Cuboid = 4cm

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★ Using the formula

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$\boxed{\tt{\bigstar{Surface\: Area\: of\: Cuboid = 2(lb + bh + hl){\bigstar}}}}$

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$\small\tt:\implies\: \: \: \: \: \: \: \: {Surface\: Area = 2(8 \times 4 + 4 \times 4 + 4 \times 8)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Surface\: Area = 2(32 + 16 + 32)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Surface\: Area = 2 \times 80}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Surface\: Area = 160cm^2}$

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Hence, the surface area of the resulting cuboid is 160 cm².

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