Question

Two Cubes, Each Of Volume $512c{m}^3$ Are Joined End To End. Find The Lateral And Total Surface Areas Of The Resulting Cuboid.

Answer 1

Finding the Lateral And Total Surface Areas Of The Resulting Cuboid.:

Volume of cube$=l^3$

$$\begin{gathered} l^3=512c{m}^3 \\ l=\sqrt{512} \\ l=8cm \end{gathered}$$

Therefore, the side is $8cm$

when we join two cubes, we will get a cuboid whose length is $16cm$

Therefore:

Height,$h=8$

Breadth,$b=8$

Total surface area of cuboid

$\begin{array}{rcl}& =& 2\times \left(lh+bh+lb\right)\\ & =& 2\times \left(128+64+128\right)\\ & =& 2\times \left(230\right)\\ & =& 640c{m}^2\end{array}$

The lateral surface area of cuboid

$$\begin{gathered} =2h\left(l+b\right) \\ =2\times 8\left(16+8\right) \\ =16\times \left(24\right) \\ =384c{m}^2 \end{gathered}$$

Therefore the Total surface area of cuboid is $\begin{array}{l}640c{m}^2\end{array}$. and the lateral surface area of cuboid is $384c{m}^2$