Question

2 cubes each of volume 64cm^3 are joined end to end .Find the surface area of the resulting cuboid.

Answer 1

GIVEN:

• 2 cubes each of volume 64cm^3 are joined end to end.

TO FIND:

• What is the surface area of resulting cuboid ?

SOLUTION:

Let the side of the cube be 'x' cm

We know that the formula for finding the volume of cube is:-

$\large{\boxed{\bf{\star \: VOLUME = (Side)^3 \: \star}}}$

According to question:-

$\sf{\longmapsto 64 = (x)^3 }$

$\sf{\longmapsto 64 = x^3 }$

$\sf{\longmapsto \sqrt{ 4 \times 4 \times 4 } = x }$

$\bf{\longmapsto 4 \: cm = x}$

Dimensions of resulting cuboid are:-

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

To find the TSA of cuboid, we use the formula:-

$\large{\boxed{\bf{\star \: TSA = 2(lb +bh+hl) \: \star}}}$

According to Question:-

$\sf{\longmapsto TSA = 2(8 \times 4 + 4 \times 4 + 4 \times 8 )}$

$\sf{\longmapsto TSA = 2(32+16+32)}$

$\sf{\longmapsto TSA = 2(80) }$

$\bf{\longmapsto TSA = 160 \: cm^2 }$

❝ Hence, the TSA of cuboid is 160 cm² ❞

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